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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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3 讲：不确定性下的决策",[1794,1795,1796],"h2",{"id":1796},"本章导学",[1798,1799,1800],"p",{},"前两章默认消费者知道每个选择会带来什么结果，但现实中的投资、保险、医疗和职业选择都带有风险。本章的核心是把“结果不确定”纳入选择模型，并理解风险规避为什么会改变需求、价格和合约形式。",[1798,1802,1803],{},"学完本章后，你应当能够：",[1805,1806,1807,1811,1814,1817],"ul",{},[1808,1809,1810],"li",{},"用彩票和状态空间描述不确定性决策问题。",[1808,1812,1813],{},"解释 vNM 期望效用理论的公理、结论和局限。",[1808,1815,1816],{},"计算确定性等价、风险溢价以及阿罗-普拉特风险规避测度。",[1808,1818,1819],{},"分析公平保险、非公平保险、自负额和资产组合选择的最优条件。",[1798,1821,1822],{},"常见题目会给定一个财富效用函数和若干随机结果，要求你比较彩票、计算风险溢价或求最优保险购买量。答题时要分清“财富的期望值”和“效用的期望值”，这是本章最容易出错的地方。",[1798,1824,1825,1826,1831,1832,1836,1837,1841],{},"本章从",[1827,1828,1830],"a",{"href":1829},"..\u002F02-comparative-statics\u002F","第 2 章","的福利测度自然过渡而来，也为",[1827,1833,1835],{"href":1834},"..\u002F07-information-economics\u002F","第 7 章","的保险市场逆向选择和道德风险埋下伏笔。行为经济学中的前景理论会在",[1827,1838,1840],{"href":1839},"..\u002F09-behavioural-economics\u002F","第 9 章","重新挑战这里的标准模型。",[1794,1843,1845],{"id":1844},"经济动机-economic-motivation","经济动机 (Economic Motivation)",[1798,1847,1848],{},"生活充满了不确定性。无论是投资股票、购买保险，还是选择职业道路，我们都需要在结果未知的情况下做出决策。理解人们如何在风险和不确定性下做选择，对于金融、保险和许多其他领域至关重要。",[1798,1850,1851],{},"传统的消费者理论假设决策者面对确定的结果，但现实中：",[1805,1853,1854,1857,1860,1863],{},[1808,1855,1856],{},"投资者不知道股票明天会涨还是跌",[1808,1858,1859],{},"购房者不确定未来房价走势",[1808,1861,1862],{},"农民不知道今年的收成如何",[1808,1864,1865],{},"创业者面临企业成败的不确定性",[1798,1867,1868],{},"这一章我们将学习如何在数学上严格地刻画和分析这类决策问题。",[1870,1871],"hr",{},[1794,1873,1875],{"id":1874},"_1-期望效用理论的公理化基础","1. 期望效用理论的公理化基础",[1877,1878,1880],"h3",{"id":1879},"_11-基本框架","1.1 基本框架",[1798,1882,1883,1887,1888,1934],{},[1884,1885,1886],"strong",{},"彩票 (Lottery)",": 一个彩票",[1889,1890,1893,1915],"span",{"className":1891},[1892],"katex",[1889,1894,1897],{"className":1895},[1896],"katex-mathml",[1898,1899,1901],"math",{"xmlns":1900},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1902,1903,1904,1911],"semantics",{},[1905,1906,1907],"mrow",{},[1908,1909,1910],"mi",{},"L",[1912,1913,1910],"annotation",{"encoding":1914},"application\u002Fx-tex",[1889,1916,1920],{"className":1917,"ariaHidden":1919},[1918],"katex-html","true",[1889,1921,1924,1929],{"className":1922},[1923],"base",[1889,1925],{"className":1926,"style":1928},[1927],"strut","height:0.6833em;",[1889,1930,1910],{"className":1931},[1932,1933],"mord","mathnormal","是对可能结果的概率分布。例如：",[1889,1936,1939],{"className":1937},[1938],"katex-display",[1889,1940,1942,2027],{"className":1941},[1892],[1889,1943,1945],{"className":1944},[1896],[1898,1946,1948],{"xmlns":1900,"display":1947},"block",[1902,1949,1950,2024],{},[1905,1951,1952,1954,1958,1962,1972,1975,1981,1984,1991,1993,1999,2001,2004,2006,2013,2015,2021],{},[1908,1953,1910],{},[1955,1956,1957],"mo",{},"=",[1955,1959,1961],{"stretchy":1960},"false","(",[1963,1964,1965,1968],"msub",{},[1908,1966,1967],{},"x",[1969,1970,1971],"mn",{},"1",[1955,1973,1974],{"separator":1919},",",[1963,1976,1977,1979],{},[1908,1978,1798],{},[1969,1980,1971],{},[1955,1982,1983],{"separator":1919},";",[1963,1985,1986,1988],{},[1908,1987,1967],{},[1969,1989,1990],{},"2",[1955,1992,1974],{"separator":1919},[1963,1994,1995,1997],{},[1908,1996,1798],{},[1969,1998,1990],{},[1955,2000,1983],{"separator":1919},[1955,2002,2003],{},"…",[1955,2005,1983],{"separator":1919},[1963,2007,2008,2010],{},[1908,2009,1967],{},[1908,2011,2012],{},"n",[1955,2014,1974],{"separator":1919},[1963,2016,2017,2019],{},[1908,2018,1798],{},[1908,2020,2012],{},[1955,2022,2023],{"stretchy":1960},")",[1912,2025,2026],{"encoding":1914},"L = (x_1, p_1; x_2, p_2; \\ldots; x_n, p_n)",[1889,2028,2030,2051],{"className":2029,"ariaHidden":1919},[1918],[1889,2031,2033,2036,2039,2044,2048],{"className":2032},[1923],[1889,2034],{"className":2035,"style":1928},[1927],[1889,2037,1910],{"className":2038},[1932,1933],[1889,2040],{"className":2041,"style":2043},[2042],"mspace","margin-right:0.2778em;",[1889,2045,1957],{"className":2046},[2047],"mrel",[1889,2049],{"className":2050,"style":2043},[2042],[1889,2052,2054,2058,2062,2118,2122,2126,2166,2169,2172,2212,2215,2218,2258,2261,2264,2268,2271,2274,2277,2318,2321,2324,2364],{"className":2053},[1923],[1889,2055],{"className":2056,"style":2057},[1927],"height:1em;vertical-align:-0.25em;",[1889,2059,1961],{"className":2060},[2061],"mopen",[1889,2063,2065,2068],{"className":2064},[1932],[1889,2066,1967],{"className":2067},[1932,1933],[1889,2069,2072],{"className":2070},[2071],"msupsub",[1889,2073,2077,2109],{"className":2074},[2075,2076],"vlist-t","vlist-t2",[1889,2078,2081,2104],{"className":2079},[2080],"vlist-r",[1889,2082,2086],{"className":2083,"style":2085},[2084],"vlist","height:0.3011em;",[1889,2087,2089,2094],{"style":2088},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1889,2090],{"className":2091,"style":2093},[2092],"pstrut","height:2.7em;",[1889,2095,2101],{"className":2096},[2097,2098,2099,2100],"sizing","reset-size6","size3","mtight",[1889,2102,1971],{"className":2103},[1932,2100],[1889,2105,2108],{"className":2106},[2107],"vlist-s","​",[1889,2110,2112],{"className":2111},[2080],[1889,2113,2116],{"className":2114,"style":2115},[2084],"height:0.15em;",[1889,2117],{},[1889,2119,1974],{"className":2120},[2121],"mpunct",[1889,2123],{"className":2124,"style":2125},[2042],"margin-right:0.1667em;",[1889,2127,2129,2132],{"className":2128},[1932],[1889,2130,1798],{"className":2131},[1932,1933],[1889,2133,2135],{"className":2134},[2071],[1889,2136,2138,2158],{"className":2137},[2075,2076],[1889,2139,2141,2155],{"className":2140},[2080],[1889,2142,2144],{"className":2143,"style":2085},[2084],[1889,2145,2146,2149],{"style":2088},[1889,2147],{"className":2148,"style":2093},[2092],[1889,2150,2152],{"className":2151},[2097,2098,2099,2100],[1889,2153,1971],{"className":2154},[1932,2100],[1889,2156,2108],{"className":2157},[2107],[1889,2159,2161],{"className":2160},[2080],[1889,2162,2164],{"className":2163,"style":2115},[2084],[1889,2165],{},[1889,2167,1983],{"className":2168},[2121],[1889,2170],{"className":2171,"style":2125},[2042],[1889,2173,2175,2178],{"className":2174},[1932],[1889,2176,1967],{"className":2177},[1932,1933],[1889,2179,2181],{"className":2180},[2071],[1889,2182,2184,2204],{"className":2183},[2075,2076],[1889,2185,2187,2201],{"className":2186},[2080],[1889,2188,2190],{"className":2189,"style":2085},[2084],[1889,2191,2192,2195],{"style":2088},[1889,2193],{"className":2194,"style":2093},[2092],[1889,2196,2198],{"className":2197},[2097,2098,2099,2100],[1889,2199,1990],{"className":2200},[1932,2100],[1889,2202,2108],{"className":2203},[2107],[1889,2205,2207],{"className":2206},[2080],[1889,2208,2210],{"className":2209,"style":2115},[2084],[1889,2211],{},[1889,2213,1974],{"className":2214},[2121],[1889,2216],{"className":2217,"style":2125},[2042],[1889,2219,2221,2224],{"className":2220},[1932],[1889,2222,1798],{"className":2223},[1932,1933],[1889,2225,2227],{"className":2226},[2071],[1889,2228,2230,2250],{"className":2229},[2075,2076],[1889,2231,2233,2247],{"className":2232},[2080],[1889,2234,2236],{"className":2235,"style":2085},[2084],[1889,2237,2238,2241],{"style":2088},[1889,2239],{"className":2240,"style":2093},[2092],[1889,2242,2244],{"className":2243},[2097,2098,2099,2100],[1889,2245,1990],{"className":2246},[1932,2100],[1889,2248,2108],{"className":2249},[2107],[1889,2251,2253],{"className":2252},[2080],[1889,2254,2256],{"className":2255,"style":2115},[2084],[1889,2257],{},[1889,2259,1983],{"className":2260},[2121],[1889,2262],{"className":2263,"style":2125},[2042],[1889,2265,2003],{"className":2266},[2267],"minner",[1889,2269],{"className":2270,"style":2125},[2042],[1889,2272,1983],{"className":2273},[2121],[1889,2275],{"className":2276,"style":2125},[2042],[1889,2278,2280,2283],{"className":2279},[1932],[1889,2281,1967],{"className":2282},[1932,1933],[1889,2284,2286],{"className":2285},[2071],[1889,2287,2289,2310],{"className":2288},[2075,2076],[1889,2290,2292,2307],{"className":2291},[2080],[1889,2293,2296],{"className":2294,"style":2295},[2084],"height:0.1514em;",[1889,2297,2298,2301],{"style":2088},[1889,2299],{"className":2300,"style":2093},[2092],[1889,2302,2304],{"className":2303},[2097,2098,2099,2100],[1889,2305,2012],{"className":2306},[1932,1933,2100],[1889,2308,2108],{"className":2309},[2107],[1889,2311,2313],{"className":2312},[2080],[1889,2314,2316],{"className":2315,"style":2115},[2084],[1889,2317],{},[1889,2319,1974],{"className":2320},[2121],[1889,2322],{"className":2323,"style":2125},[2042],[1889,2325,2327,2330],{"className":2326},[1932],[1889,2328,1798],{"className":2329},[1932,1933],[1889,2331,2333],{"className":2332},[2071],[1889,2334,2336,2356],{"className":2335},[2075,2076],[1889,2337,2339,2353],{"className":2338},[2080],[1889,2340,2342],{"className":2341,"style":2295},[2084],[1889,2343,2344,2347],{"style":2088},[1889,2345],{"className":2346,"style":2093},[2092],[1889,2348,2350],{"className":2349},[2097,2098,2099,2100],[1889,2351,2012],{"className":2352},[1932,1933,2100],[1889,2354,2108],{"className":2355},[2107],[1889,2357,2359],{"className":2358},[2080],[1889,2360,2362],{"className":2361,"style":2115},[2084],[1889,2363],{},[1889,2365,2023],{"className":2366},[2367],"mclose",[1798,2369,2370,2371,2444,2445,2516,2517,2698],{},"表示以概率",[1889,2372,2374,2393],{"className":2373},[1892],[1889,2375,2377],{"className":2376},[1896],[1898,2378,2379],{"xmlns":1900},[1902,2380,2381,2390],{},[1905,2382,2383],{},[1963,2384,2385,2387],{},[1908,2386,1798],{},[1908,2388,2389],{},"i",[1912,2391,2392],{"encoding":1914},"p_i",[1889,2394,2396],{"className":2395,"ariaHidden":1919},[1918],[1889,2397,2399,2403],{"className":2398},[1923],[1889,2400],{"className":2401,"style":2402},[1927],"height:0.625em;vertical-align:-0.1944em;",[1889,2404,2406,2409],{"className":2405},[1932],[1889,2407,1798],{"className":2408},[1932,1933],[1889,2410,2412],{"className":2411},[2071],[1889,2413,2415,2436],{"className":2414},[2075,2076],[1889,2416,2418,2433],{"className":2417},[2080],[1889,2419,2422],{"className":2420,"style":2421},[2084],"height:0.3117em;",[1889,2423,2424,2427],{"style":2088},[1889,2425],{"className":2426,"style":2093},[2092],[1889,2428,2430],{"className":2429},[2097,2098,2099,2100],[1889,2431,2389],{"className":2432},[1932,1933,2100],[1889,2434,2108],{"className":2435},[2107],[1889,2437,2439],{"className":2438},[2080],[1889,2440,2442],{"className":2441,"style":2115},[2084],[1889,2443],{},"获得结果",[1889,2446,2448,2466],{"className":2447},[1892],[1889,2449,2451],{"className":2450},[1896],[1898,2452,2453],{"xmlns":1900},[1902,2454,2455,2463],{},[1905,2456,2457],{},[1963,2458,2459,2461],{},[1908,2460,1967],{},[1908,2462,2389],{},[1912,2464,2465],{"encoding":1914},"x_i",[1889,2467,2469],{"className":2468,"ariaHidden":1919},[1918],[1889,2470,2472,2476],{"className":2471},[1923],[1889,2473],{"className":2474,"style":2475},[1927],"height:0.5806em;vertical-align:-0.15em;",[1889,2477,2479,2482],{"className":2478},[1932],[1889,2480,1967],{"className":2481},[1932,1933],[1889,2483,2485],{"className":2484},[2071],[1889,2486,2488,2508],{"className":2487},[2075,2076],[1889,2489,2491,2505],{"className":2490},[2080],[1889,2492,2494],{"className":2493,"style":2421},[2084],[1889,2495,2496,2499],{"style":2088},[1889,2497],{"className":2498,"style":2093},[2092],[1889,2500,2502],{"className":2501},[2097,2098,2099,2100],[1889,2503,2389],{"className":2504},[1932,1933,2100],[1889,2506,2108],{"className":2507},[2107],[1889,2509,2511],{"className":2510},[2080],[1889,2512,2514],{"className":2513,"style":2115},[2084],[1889,2515],{},"，其中",[1889,2518,2520,2558],{"className":2519},[1892],[1889,2521,2523],{"className":2522},[1896],[1898,2524,2525],{"xmlns":1900},[1902,2526,2527,2555],{},[1905,2528,2529,2545,2551,2553],{},[2530,2531,2532,2535,2543],"msubsup",{},[1955,2533,2534],{},"∑",[1905,2536,2537,2539,2541],{},[1908,2538,2389],{},[1955,2540,1957],{},[1969,2542,1971],{},[1908,2544,2012],{},[1963,2546,2547,2549],{},[1908,2548,1798],{},[1908,2550,2389],{},[1955,2552,1957],{},[1969,2554,1971],{},[1912,2556,2557],{"encoding":1914},"\\sum_{i=1}^n p_i = 1",[1889,2559,2561,2688],{"className":2560,"ariaHidden":1919},[1918],[1889,2562,2564,2568,2636,2639,2679,2682,2685],{"className":2563},[1923],[1889,2565],{"className":2566,"style":2567},[1927],"height:1.104em;vertical-align:-0.2997em;",[1889,2569,2572,2578],{"className":2570},[2571],"mop",[1889,2573,2534],{"className":2574,"style":2577},[2571,2575,2576],"op-symbol","small-op","position:relative;top:0em;",[1889,2579,2581],{"className":2580},[2071],[1889,2582,2584,2627],{"className":2583},[2075,2076],[1889,2585,2587,2624],{"className":2586},[2080],[1889,2588,2591,2612],{"className":2589,"style":2590},[2084],"height:0.8043em;",[1889,2592,2594,2597],{"style":2593},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1889,2595],{"className":2596,"style":2093},[2092],[1889,2598,2600],{"className":2599},[2097,2098,2099,2100],[1889,2601,2603,2606,2609],{"className":2602},[1932,2100],[1889,2604,2389],{"className":2605},[1932,1933,2100],[1889,2607,1957],{"className":2608},[2047,2100],[1889,2610,1971],{"className":2611},[1932,2100],[1889,2613,2615,2618],{"style":2614},"top:-3.2029em;margin-right:0.05em;",[1889,2616],{"className":2617,"style":2093},[2092],[1889,2619,2621],{"className":2620},[2097,2098,2099,2100],[1889,2622,2012],{"className":2623},[1932,1933,2100],[1889,2625,2108],{"className":2626},[2107],[1889,2628,2630],{"className":2629},[2080],[1889,2631,2634],{"className":2632,"style":2633},[2084],"height:0.2997em;",[1889,2635],{},[1889,2637],{"className":2638,"style":2125},[2042],[1889,2640,2642,2645],{"className":2641},[1932],[1889,2643,1798],{"className":2644},[1932,1933],[1889,2646,2648],{"className":2647},[2071],[1889,2649,2651,2671],{"className":2650},[2075,2076],[1889,2652,2654,2668],{"className":2653},[2080],[1889,2655,2657],{"className":2656,"style":2421},[2084],[1889,2658,2659,2662],{"style":2088},[1889,2660],{"className":2661,"style":2093},[2092],[1889,2663,2665],{"className":2664},[2097,2098,2099,2100],[1889,2666,2389],{"className":2667},[1932,1933,2100],[1889,2669,2108],{"className":2670},[2107],[1889,2672,2674],{"className":2673},[2080],[1889,2675,2677],{"className":2676,"style":2115},[2084],[1889,2678],{},[1889,2680],{"className":2681,"style":2043},[2042],[1889,2683,1957],{"className":2684},[2047],[1889,2686],{"className":2687,"style":2043},[2042],[1889,2689,2691,2695],{"className":2690},[1923],[1889,2692],{"className":2693,"style":2694},[1927],"height:0.6444em;",[1889,2696,1971],{"className":2697},[1932],"。",[1798,2700,2701,2704],{},[1884,2702,2703],{},"简单例子",":",[1805,2706,2707,2717],{},[1808,2708,2709,2716],{},[1889,2710,2715],{"className":2711,"title":2713,"style":2714},[2712],"katex-error","ParseError: KaTeX parse error: Unexpected character: '\\' at position 8: L_1 = (\\̲","color:#cc0000","L_1 = (\\","100, 0.5; $0, 0.5)$：抛硬币赌博，正面赢100元，反面什么都没有",[1808,2718,2719,2724],{},[1889,2720,2723],{"className":2721,"title":2722,"style":2714},[2712],"ParseError: KaTeX parse error: Unexpected character: '\\' at position 8: L_2 = (\\̲","L_2 = (\\","50, 1)$：确定获得50元",[1798,2726,2727],{},"理性的决策者会选择哪个？这取决于其对风险的态度。",[1877,2729,2731],{"id":2730},"_12-冯诺依曼-摩根斯特恩-vnm-公理","1.2 冯·诺依曼-摩根斯特恩 (vNM) 公理",[1798,2733,2734],{},"期望效用理论建立在四个理性公理之上：",[1798,2736,2737,2740,2741,2769,2770,2838,2839,2867,2868,2929],{},[1884,2738,2739],{},"公理1: 完备性 (Completeness)","\n对于任意两个彩票",[1889,2742,2744,2757],{"className":2743},[1892],[1889,2745,2747],{"className":2746},[1896],[1898,2748,2749],{"xmlns":1900},[1902,2750,2751,2755],{},[1905,2752,2753],{},[1908,2754,1910],{},[1912,2756,1910],{"encoding":1914},[1889,2758,2760],{"className":2759,"ariaHidden":1919},[1918],[1889,2761,2763,2766],{"className":2762},[1923],[1889,2764],{"className":2765,"style":1928},[1927],[1889,2767,1910],{"className":2768},[1932,1933],"和",[1889,2771,2773,2795],{"className":2772},[1892],[1889,2774,2776],{"className":2775},[1896],[1898,2777,2778],{"xmlns":1900},[1902,2779,2780,2792],{},[1905,2781,2782],{},[2783,2784,2785,2787],"msup",{},[1908,2786,1910],{},[1955,2788,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},"normal","0em","′",[1912,2793,2794],{"encoding":1914},"L'",[1889,2796,2798],{"className":2797,"ariaHidden":1919},[1918],[1889,2799,2801,2805],{"className":2800},[1923],[1889,2802],{"className":2803,"style":2804},[1927],"height:0.7519em;",[1889,2806,2808,2811],{"className":2807},[1932],[1889,2809,1910],{"className":2810},[1932,1933],[1889,2812,2814],{"className":2813},[2071],[1889,2815,2817],{"className":2816},[2075],[1889,2818,2820],{"className":2819},[2080],[1889,2821,2823],{"className":2822,"style":2804},[2084],[1889,2824,2826,2829],{"style":2825},"top:-3.063em;margin-right:0.05em;",[1889,2827],{"className":2828,"style":2093},[2092],[1889,2830,2832],{"className":2831},[2097,2098,2099,2100],[1889,2833,2835],{"className":2834},[1932,2100],[1889,2836,2791],{"className":2837},[1932,2100],"，决策者要么偏好",[1889,2840,2842,2855],{"className":2841},[1892],[1889,2843,2845],{"className":2844},[1896],[1898,2846,2847],{"xmlns":1900},[1902,2848,2849,2853],{},[1905,2850,2851],{},[1908,2852,1910],{},[1912,2854,1910],{"encoding":1914},[1889,2856,2858],{"className":2857,"ariaHidden":1919},[1918],[1889,2859,2861,2864],{"className":2860},[1923],[1889,2862],{"className":2863,"style":1928},[1927],[1889,2865,1910],{"className":2866},[1932,1933],"，要么偏好",[1889,2869,2871,2888],{"className":2870},[1892],[1889,2872,2874],{"className":2873},[1896],[1898,2875,2876],{"xmlns":1900},[1902,2877,2878,2886],{},[1905,2879,2880],{},[2783,2881,2882,2884],{},[1908,2883,1910],{},[1955,2885,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1912,2887,2794],{"encoding":1914},[1889,2889,2891],{"className":2890,"ariaHidden":1919},[1918],[1889,2892,2894,2897],{"className":2893},[1923],[1889,2895],{"className":2896,"style":2804},[1927],[1889,2898,2900,2903],{"className":2899},[1932],[1889,2901,1910],{"className":2902},[1932,1933],[1889,2904,2906],{"className":2905},[2071],[1889,2907,2909],{"className":2908},[2075],[1889,2910,2912],{"className":2911},[2080],[1889,2913,2915],{"className":2914,"style":2804},[2084],[1889,2916,2917,2920],{"style":2825},[1889,2918],{"className":2919,"style":2093},[2092],[1889,2921,2923],{"className":2922},[2097,2098,2099,2100],[1889,2924,2926],{"className":2925},[1932,2100],[1889,2927,2791],{"className":2928},[1932,2100],"，要么对两者无差异。",[1889,2931,2933],{"className":2932},[1938],[1889,2934,2936,2995],{"className":2935},[1892],[1889,2937,2939],{"className":2938},[1896],[1898,2940,2941],{"xmlns":1900,"display":1947},[1902,2942,2943,2992],{},[1905,2944,2945,2947,2950,2956,2959,2963,2965,2971,2973,2975,2977,2979,2981,2983,2986],{},[1908,2946,1910],{},[1955,2948,2949],{},"⪰",[2783,2951,2952,2954],{},[1908,2953,1910],{},[1955,2955,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[2042,2957],{"width":2958},"1em",[2960,2961,2962],"mtext",{},"或",[2042,2964],{"width":2958},[2783,2966,2967,2969],{},[1908,2968,1910],{},[1955,2970,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,2972,2949],{},[1908,2974,1910],{},[2042,2976],{"width":2958},[2960,2978,2962],{},[2042,2980],{"width":2958},[1908,2982,1910],{},[1955,2984,2985],{},"∼",[2783,2987,2988,2990],{},[1908,2989,1910],{},[1955,2991,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1912,2993,2994],{"encoding":1914},"L \\succeq L' \\quad \\text{或} \\quad L' \\succeq L \\quad \\text{或} \\quad L \\sim L'",[1889,2996,2998,3017,3114,3147],{"className":2997,"ariaHidden":1919},[1918],[1889,2999,3001,3005,3008,3011,3014],{"className":3000},[1923],[1889,3002],{"className":3003,"style":3004},[1927],"height:0.8193em;vertical-align:-0.136em;",[1889,3006,1910],{"className":3007},[1932,1933],[1889,3009],{"className":3010,"style":2043},[2042],[1889,3012,2949],{"className":3013},[2047],[1889,3015],{"className":3016,"style":2043},[2042],[1889,3018,3020,3024,3058,3062,3070,3073,3105,3108,3111],{"className":3019},[1923],[1889,3021],{"className":3022,"style":3023},[1927],"height:0.9379em;vertical-align:-0.136em;",[1889,3025,3027,3030],{"className":3026},[1932],[1889,3028,1910],{"className":3029},[1932,1933],[1889,3031,3033],{"className":3032},[2071],[1889,3034,3036],{"className":3035},[2075],[1889,3037,3039],{"className":3038},[2080],[1889,3040,3043],{"className":3041,"style":3042},[2084],"height:0.8019em;",[1889,3044,3046,3049],{"style":3045},"top:-3.113em;margin-right:0.05em;",[1889,3047],{"className":3048,"style":2093},[2092],[1889,3050,3052],{"className":3051},[2097,2098,2099,2100],[1889,3053,3055],{"className":3054},[1932,2100],[1889,3056,2791],{"className":3057},[1932,2100],[1889,3059],{"className":3060,"style":3061},[2042],"margin-right:1em;",[1889,3063,3066],{"className":3064},[1932,3065],"text",[1889,3067,2962],{"className":3068},[1932,3069],"cjk_fallback",[1889,3071],{"className":3072,"style":3061},[2042],[1889,3074,3076,3079],{"className":3075},[1932],[1889,3077,1910],{"className":3078},[1932,1933],[1889,3080,3082],{"className":3081},[2071],[1889,3083,3085],{"className":3084},[2075],[1889,3086,3088],{"className":3087},[2080],[1889,3089,3091],{"className":3090,"style":3042},[2084],[1889,3092,3093,3096],{"style":3045},[1889,3094],{"className":3095,"style":2093},[2092],[1889,3097,3099],{"className":3098},[2097,2098,2099,2100],[1889,3100,3102],{"className":3101},[1932,2100],[1889,3103,2791],{"className":3104},[1932,2100],[1889,3106],{"className":3107,"style":2043},[2042],[1889,3109,2949],{"className":3110},[2047],[1889,3112],{"className":3113,"style":2043},[2042],[1889,3115,3117,3120,3123,3126,3132,3135,3138,3141,3144],{"className":3116},[1923],[1889,3118],{"className":3119,"style":1928},[1927],[1889,3121,1910],{"className":3122},[1932,1933],[1889,3124],{"className":3125,"style":3061},[2042],[1889,3127,3129],{"className":3128},[1932,3065],[1889,3130,2962],{"className":3131},[1932,3069],[1889,3133],{"className":3134,"style":3061},[2042],[1889,3136,1910],{"className":3137},[1932,1933],[1889,3139],{"className":3140,"style":2043},[2042],[1889,3142,2985],{"className":3143},[2047],[1889,3145],{"className":3146,"style":2043},[2042],[1889,3148,3150,3153],{"className":3149},[1923],[1889,3151],{"className":3152,"style":3042},[1927],[1889,3154,3156,3159],{"className":3155},[1932],[1889,3157,1910],{"className":3158},[1932,1933],[1889,3160,3162],{"className":3161},[2071],[1889,3163,3165],{"className":3164},[2075],[1889,3166,3168],{"className":3167},[2080],[1889,3169,3171],{"className":3170,"style":3042},[2084],[1889,3172,3173,3176],{"style":3045},[1889,3174],{"className":3175,"style":2093},[2092],[1889,3177,3179],{"className":3178},[2097,2098,2099,2100],[1889,3180,3182],{"className":3181},[1932,2100],[1889,3183,2791],{"className":3184},[1932,2100],[1798,3186,3187,3190,3191,3325,3326,3460,3461,2698],{},[1884,3188,3189],{},"公理2: 传递性 (Transitivity)","\n如果",[1889,3192,3194,3220],{"className":3193},[1892],[1889,3195,3197],{"className":3196},[1896],[1898,3198,3199],{"xmlns":1900},[1902,3200,3201,3217],{},[1905,3202,3203,3209,3211],{},[1963,3204,3205,3207],{},[1908,3206,1910],{},[1969,3208,1971],{},[1955,3210,2949],{},[1963,3212,3213,3215],{},[1908,3214,1910],{},[1969,3216,1990],{},[1912,3218,3219],{"encoding":1914},"L_1 \\succeq L_2",[1889,3221,3223,3279],{"className":3222,"ariaHidden":1919},[1918],[1889,3224,3226,3230,3270,3273,3276],{"className":3225},[1923],[1889,3227],{"className":3228,"style":3229},[1927],"height:0.8333em;vertical-align:-0.15em;",[1889,3231,3233,3236],{"className":3232},[1932],[1889,3234,1910],{"className":3235},[1932,1933],[1889,3237,3239],{"className":3238},[2071],[1889,3240,3242,3262],{"className":3241},[2075,2076],[1889,3243,3245,3259],{"className":3244},[2080],[1889,3246,3248],{"className":3247,"style":2085},[2084],[1889,3249,3250,3253],{"style":2088},[1889,3251],{"className":3252,"style":2093},[2092],[1889,3254,3256],{"className":3255},[2097,2098,2099,2100],[1889,3257,1971],{"className":3258},[1932,2100],[1889,3260,2108],{"className":3261},[2107],[1889,3263,3265],{"className":3264},[2080],[1889,3266,3268],{"className":3267,"style":2115},[2084],[1889,3269],{},[1889,3271],{"className":3272,"style":2043},[2042],[1889,3274,2949],{"className":3275},[2047],[1889,3277],{"className":3278,"style":2043},[2042],[1889,3280,3282,3285],{"className":3281},[1923],[1889,3283],{"className":3284,"style":3229},[1927],[1889,3286,3288,3291],{"className":3287},[1932],[1889,3289,1910],{"className":3290},[1932,1933],[1889,3292,3294],{"className":3293},[2071],[1889,3295,3297,3317],{"className":3296},[2075,2076],[1889,3298,3300,3314],{"className":3299},[2080],[1889,3301,3303],{"className":3302,"style":2085},[2084],[1889,3304,3305,3308],{"style":2088},[1889,3306],{"className":3307,"style":2093},[2092],[1889,3309,3311],{"className":3310},[2097,2098,2099,2100],[1889,3312,1990],{"className":3313},[1932,2100],[1889,3315,2108],{"className":3316},[2107],[1889,3318,3320],{"className":3319},[2080],[1889,3321,3323],{"className":3322,"style":2115},[2084],[1889,3324],{},"且",[1889,3327,3329,3356],{"className":3328},[1892],[1889,3330,3332],{"className":3331},[1896],[1898,3333,3334],{"xmlns":1900},[1902,3335,3336,3353],{},[1905,3337,3338,3344,3346],{},[1963,3339,3340,3342],{},[1908,3341,1910],{},[1969,3343,1990],{},[1955,3345,2949],{},[1963,3347,3348,3350],{},[1908,3349,1910],{},[1969,3351,3352],{},"3",[1912,3354,3355],{"encoding":1914},"L_2 \\succeq L_3",[1889,3357,3359,3414],{"className":3358,"ariaHidden":1919},[1918],[1889,3360,3362,3365,3405,3408,3411],{"className":3361},[1923],[1889,3363],{"className":3364,"style":3229},[1927],[1889,3366,3368,3371],{"className":3367},[1932],[1889,3369,1910],{"className":3370},[1932,1933],[1889,3372,3374],{"className":3373},[2071],[1889,3375,3377,3397],{"className":3376},[2075,2076],[1889,3378,3380,3394],{"className":3379},[2080],[1889,3381,3383],{"className":3382,"style":2085},[2084],[1889,3384,3385,3388],{"style":2088},[1889,3386],{"className":3387,"style":2093},[2092],[1889,3389,3391],{"className":3390},[2097,2098,2099,2100],[1889,3392,1990],{"className":3393},[1932,2100],[1889,3395,2108],{"className":3396},[2107],[1889,3398,3400],{"className":3399},[2080],[1889,3401,3403],{"className":3402,"style":2115},[2084],[1889,3404],{},[1889,3406],{"className":3407,"style":2043},[2042],[1889,3409,2949],{"className":3410},[2047],[1889,3412],{"className":3413,"style":2043},[2042],[1889,3415,3417,3420],{"className":3416},[1923],[1889,3418],{"className":3419,"style":3229},[1927],[1889,3421,3423,3426],{"className":3422},[1932],[1889,3424,1910],{"className":3425},[1932,1933],[1889,3427,3429],{"className":3428},[2071],[1889,3430,3432,3452],{"className":3431},[2075,2076],[1889,3433,3435,3449],{"className":3434},[2080],[1889,3436,3438],{"className":3437,"style":2085},[2084],[1889,3439,3440,3443],{"style":2088},[1889,3441],{"className":3442,"style":2093},[2092],[1889,3444,3446],{"className":3445},[2097,2098,2099,2100],[1889,3447,3352],{"className":3448},[1932,2100],[1889,3450,2108],{"className":3451},[2107],[1889,3453,3455],{"className":3454},[2080],[1889,3456,3458],{"className":3457,"style":2115},[2084],[1889,3459],{},"，则",[1889,3462,3464,3490],{"className":3463},[1892],[1889,3465,3467],{"className":3466},[1896],[1898,3468,3469],{"xmlns":1900},[1902,3470,3471,3487],{},[1905,3472,3473,3479,3481],{},[1963,3474,3475,3477],{},[1908,3476,1910],{},[1969,3478,1971],{},[1955,3480,2949],{},[1963,3482,3483,3485],{},[1908,3484,1910],{},[1969,3486,3352],{},[1912,3488,3489],{"encoding":1914},"L_1 \\succeq L_3",[1889,3491,3493,3548],{"className":3492,"ariaHidden":1919},[1918],[1889,3494,3496,3499,3539,3542,3545],{"className":3495},[1923],[1889,3497],{"className":3498,"style":3229},[1927],[1889,3500,3502,3505],{"className":3501},[1932],[1889,3503,1910],{"className":3504},[1932,1933],[1889,3506,3508],{"className":3507},[2071],[1889,3509,3511,3531],{"className":3510},[2075,2076],[1889,3512,3514,3528],{"className":3513},[2080],[1889,3515,3517],{"className":3516,"style":2085},[2084],[1889,3518,3519,3522],{"style":2088},[1889,3520],{"className":3521,"style":2093},[2092],[1889,3523,3525],{"className":3524},[2097,2098,2099,2100],[1889,3526,1971],{"className":3527},[1932,2100],[1889,3529,2108],{"className":3530},[2107],[1889,3532,3534],{"className":3533},[2080],[1889,3535,3537],{"className":3536,"style":2115},[2084],[1889,3538],{},[1889,3540],{"className":3541,"style":2043},[2042],[1889,3543,2949],{"className":3544},[2047],[1889,3546],{"className":3547,"style":2043},[2042],[1889,3549,3551,3554],{"className":3550},[1923],[1889,3552],{"className":3553,"style":3229},[1927],[1889,3555,3557,3560],{"className":3556},[1932],[1889,3558,1910],{"className":3559},[1932,1933],[1889,3561,3563],{"className":3562},[2071],[1889,3564,3566,3586],{"className":3565},[2075,2076],[1889,3567,3569,3583],{"className":3568},[2080],[1889,3570,3572],{"className":3571,"style":2085},[2084],[1889,3573,3574,3577],{"style":2088},[1889,3575],{"className":3576,"style":2093},[2092],[1889,3578,3580],{"className":3579},[2097,2098,2099,2100],[1889,3581,3352],{"className":3582},[1932,2100],[1889,3584,2108],{"className":3585},[2107],[1889,3587,3589],{"className":3588},[2080],[1889,3590,3592],{"className":3591,"style":2115},[2084],[1889,3593],{},[1798,3595,3596,3190,3599,3796,3797,3876],{},[1884,3597,3598],{},"公理3: 连续性 (Continuity)",[1889,3600,3602,3637],{"className":3601},[1892],[1889,3603,3605],{"className":3604},[1896],[1898,3606,3607],{"xmlns":1900},[1902,3608,3609,3634],{},[1905,3610,3611,3617,3620,3626,3628],{},[1963,3612,3613,3615],{},[1908,3614,1910],{},[1969,3616,1971],{},[1955,3618,3619],{},"≻",[1963,3621,3622,3624],{},[1908,3623,1910],{},[1969,3625,1990],{},[1955,3627,3619],{},[1963,3629,3630,3632],{},[1908,3631,1910],{},[1969,3633,3352],{},[1912,3635,3636],{"encoding":1914},"L_1 \\succ L_2 \\succ L_3",[1889,3638,3640,3695,3750],{"className":3639,"ariaHidden":1919},[1918],[1889,3641,3643,3646,3686,3689,3692],{"className":3642},[1923],[1889,3644],{"className":3645,"style":3229},[1927],[1889,3647,3649,3652],{"className":3648},[1932],[1889,3650,1910],{"className":3651},[1932,1933],[1889,3653,3655],{"className":3654},[2071],[1889,3656,3658,3678],{"className":3657},[2075,2076],[1889,3659,3661,3675],{"className":3660},[2080],[1889,3662,3664],{"className":3663,"style":2085},[2084],[1889,3665,3666,3669],{"style":2088},[1889,3667],{"className":3668,"style":2093},[2092],[1889,3670,3672],{"className":3671},[2097,2098,2099,2100],[1889,3673,1971],{"className":3674},[1932,2100],[1889,3676,2108],{"className":3677},[2107],[1889,3679,3681],{"className":3680},[2080],[1889,3682,3684],{"className":3683,"style":2115},[2084],[1889,3685],{},[1889,3687],{"className":3688,"style":2043},[2042],[1889,3690,3619],{"className":3691},[2047],[1889,3693],{"className":3694,"style":2043},[2042],[1889,3696,3698,3701,3741,3744,3747],{"className":3697},[1923],[1889,3699],{"className":3700,"style":3229},[1927],[1889,3702,3704,3707],{"className":3703},[1932],[1889,3705,1910],{"className":3706},[1932,1933],[1889,3708,3710],{"className":3709},[2071],[1889,3711,3713,3733],{"className":3712},[2075,2076],[1889,3714,3716,3730],{"className":3715},[2080],[1889,3717,3719],{"className":3718,"style":2085},[2084],[1889,3720,3721,3724],{"style":2088},[1889,3722],{"className":3723,"style":2093},[2092],[1889,3725,3727],{"className":3726},[2097,2098,2099,2100],[1889,3728,1990],{"className":3729},[1932,2100],[1889,3731,2108],{"className":3732},[2107],[1889,3734,3736],{"className":3735},[2080],[1889,3737,3739],{"className":3738,"style":2115},[2084],[1889,3740],{},[1889,3742],{"className":3743,"style":2043},[2042],[1889,3745,3619],{"className":3746},[2047],[1889,3748],{"className":3749,"style":2043},[2042],[1889,3751,3753,3756],{"className":3752},[1923],[1889,3754],{"className":3755,"style":3229},[1927],[1889,3757,3759,3762],{"className":3758},[1932],[1889,3760,1910],{"className":3761},[1932,1933],[1889,3763,3765],{"className":3764},[2071],[1889,3766,3768,3788],{"className":3767},[2075,2076],[1889,3769,3771,3785],{"className":3770},[2080],[1889,3772,3774],{"className":3773,"style":2085},[2084],[1889,3775,3776,3779],{"style":2088},[1889,3777],{"className":3778,"style":2093},[2092],[1889,3780,3782],{"className":3781},[2097,2098,2099,2100],[1889,3783,3352],{"className":3784},[1932,2100],[1889,3786,2108],{"className":3787},[2107],[1889,3789,3791],{"className":3790},[2080],[1889,3792,3794],{"className":3793,"style":2115},[2084],[1889,3795],{},"，那么存在",[1889,3798,3800,3829],{"className":3799},[1892],[1889,3801,3803],{"className":3802},[1896],[1898,3804,3805],{"xmlns":1900},[1902,3806,3807,3826],{},[1905,3808,3809,3812,3815,3817,3820,3822,3824],{},[1908,3810,3811],{},"α",[1955,3813,3814],{},"∈",[1955,3816,1961],{"stretchy":1960},[1969,3818,3819],{},"0",[1955,3821,1974],{"separator":1919},[1969,3823,1971],{},[1955,3825,2023],{"stretchy":1960},[1912,3827,3828],{"encoding":1914},"\\alpha \\in (0,1)",[1889,3830,3832,3852],{"className":3831,"ariaHidden":1919},[1918],[1889,3833,3835,3839,3843,3846,3849],{"className":3834},[1923],[1889,3836],{"className":3837,"style":3838},[1927],"height:0.5782em;vertical-align:-0.0391em;",[1889,3840,3811],{"className":3841,"style":3842},[1932,1933],"margin-right:0.0037em;",[1889,3844],{"className":3845,"style":2043},[2042],[1889,3847,3814],{"className":3848},[2047],[1889,3850],{"className":3851,"style":2043},[2042],[1889,3853,3855,3858,3861,3864,3867,3870,3873],{"className":3854},[1923],[1889,3856],{"className":3857,"style":2057},[1927],[1889,3859,1961],{"className":3860},[2061],[1889,3862,3819],{"className":3863},[1932],[1889,3865,1974],{"className":3866},[2121],[1889,3868],{"className":3869,"style":2125},[2042],[1889,3871,1971],{"className":3872},[1932],[1889,3874,2023],{"className":3875},[2367],"使得：",[1889,3878,3880],{"className":3879},[1938],[1889,3881,3883,3931],{"className":3882},[1892],[1889,3884,3886],{"className":3885},[1896],[1898,3887,3888],{"xmlns":1900,"display":1947},[1902,3889,3890,3928],{},[1905,3891,3892,3898,3900,3902,3908,3911,3913,3915,3918,3920,3922],{},[1963,3893,3894,3896],{},[1908,3895,1910],{},[1969,3897,1990],{},[1955,3899,2985],{},[1908,3901,3811],{},[1963,3903,3904,3906],{},[1908,3905,1910],{},[1969,3907,1971],{},[1955,3909,3910],{},"+",[1955,3912,1961],{"stretchy":1960},[1969,3914,1971],{},[1955,3916,3917],{},"−",[1908,3919,3811],{},[1955,3921,2023],{"stretchy":1960},[1963,3923,3924,3926],{},[1908,3925,1910],{},[1969,3927,3352],{},[1912,3929,3930],{"encoding":1914},"L_2 \\sim \\alpha L_1 + (1-\\alpha) L_3",[1889,3932,3934,3989,4049,4070],{"className":3933,"ariaHidden":1919},[1918],[1889,3935,3937,3940,3980,3983,3986],{"className":3936},[1923],[1889,3938],{"className":3939,"style":3229},[1927],[1889,3941,3943,3946],{"className":3942},[1932],[1889,3944,1910],{"className":3945},[1932,1933],[1889,3947,3949],{"className":3948},[2071],[1889,3950,3952,3972],{"className":3951},[2075,2076],[1889,3953,3955,3969],{"className":3954},[2080],[1889,3956,3958],{"className":3957,"style":2085},[2084],[1889,3959,3960,3963],{"style":2088},[1889,3961],{"className":3962,"style":2093},[2092],[1889,3964,3966],{"className":3965},[2097,2098,2099,2100],[1889,3967,1990],{"className":3968},[1932,2100],[1889,3970,2108],{"className":3971},[2107],[1889,3973,3975],{"className":3974},[2080],[1889,3976,3978],{"className":3977,"style":2115},[2084],[1889,3979],{},[1889,3981],{"className":3982,"style":2043},[2042],[1889,3984,2985],{"className":3985},[2047],[1889,3987],{"className":3988,"style":2043},[2042],[1889,3990,3992,3995,3998,4038,4042,4046],{"className":3991},[1923],[1889,3993],{"className":3994,"style":3229},[1927],[1889,3996,3811],{"className":3997,"style":3842},[1932,1933],[1889,3999,4001,4004],{"className":4000},[1932],[1889,4002,1910],{"className":4003},[1932,1933],[1889,4005,4007],{"className":4006},[2071],[1889,4008,4010,4030],{"className":4009},[2075,2076],[1889,4011,4013,4027],{"className":4012},[2080],[1889,4014,4016],{"className":4015,"style":2085},[2084],[1889,4017,4018,4021],{"style":2088},[1889,4019],{"className":4020,"style":2093},[2092],[1889,4022,4024],{"className":4023},[2097,2098,2099,2100],[1889,4025,1971],{"className":4026},[1932,2100],[1889,4028,2108],{"className":4029},[2107],[1889,4031,4033],{"className":4032},[2080],[1889,4034,4036],{"className":4035,"style":2115},[2084],[1889,4037],{},[1889,4039],{"className":4040,"style":4041},[2042],"margin-right:0.2222em;",[1889,4043,3910],{"className":4044},[4045],"mbin",[1889,4047],{"className":4048,"style":4041},[2042],[1889,4050,4052,4055,4058,4061,4064,4067],{"className":4051},[1923],[1889,4053],{"className":4054,"style":2057},[1927],[1889,4056,1961],{"className":4057},[2061],[1889,4059,1971],{"className":4060},[1932],[1889,4062],{"className":4063,"style":4041},[2042],[1889,4065,3917],{"className":4066},[4045],[1889,4068],{"className":4069,"style":4041},[2042],[1889,4071,4073,4076,4079,4082],{"className":4072},[1923],[1889,4074],{"className":4075,"style":2057},[1927],[1889,4077,3811],{"className":4078,"style":3842},[1932,1933],[1889,4080,2023],{"className":4081},[2367],[1889,4083,4085,4088],{"className":4084},[1932],[1889,4086,1910],{"className":4087},[1932,1933],[1889,4089,4091],{"className":4090},[2071],[1889,4092,4094,4114],{"className":4093},[2075,2076],[1889,4095,4097,4111],{"className":4096},[2080],[1889,4098,4100],{"className":4099,"style":2085},[2084],[1889,4101,4102,4105],{"style":2088},[1889,4103],{"className":4104,"style":2093},[2092],[1889,4106,4108],{"className":4107},[2097,2098,2099,2100],[1889,4109,3352],{"className":4110},[1932,2100],[1889,4112,2108],{"className":4113},[2107],[1889,4115,4117],{"className":4116},[2080],[1889,4118,4120],{"className":4119,"style":2115},[2084],[1889,4121],{},[1798,4123,4124,4127,4128,4198,4199,2769,4269,4339,4340,4409,4410,4479,4480,4549],{},[1884,4125,4126],{},"直觉",": 如果",[1889,4129,4131,4149],{"className":4130},[1892],[1889,4132,4134],{"className":4133},[1896],[1898,4135,4136],{"xmlns":1900},[1902,4137,4138,4146],{},[1905,4139,4140],{},[1963,4141,4142,4144],{},[1908,4143,1910],{},[1969,4145,1990],{},[1912,4147,4148],{"encoding":1914},"L_2",[1889,4150,4152],{"className":4151,"ariaHidden":1919},[1918],[1889,4153,4155,4158],{"className":4154},[1923],[1889,4156],{"className":4157,"style":3229},[1927],[1889,4159,4161,4164],{"className":4160},[1932],[1889,4162,1910],{"className":4163},[1932,1933],[1889,4165,4167],{"className":4166},[2071],[1889,4168,4170,4190],{"className":4169},[2075,2076],[1889,4171,4173,4187],{"className":4172},[2080],[1889,4174,4176],{"className":4175,"style":2085},[2084],[1889,4177,4178,4181],{"style":2088},[1889,4179],{"className":4180,"style":2093},[2092],[1889,4182,4184],{"className":4183},[2097,2098,2099,2100],[1889,4185,1990],{"className":4186},[1932,2100],[1889,4188,2108],{"className":4189},[2107],[1889,4191,4193],{"className":4192},[2080],[1889,4194,4196],{"className":4195,"style":2115},[2084],[1889,4197],{},"介于",[1889,4200,4202,4220],{"className":4201},[1892],[1889,4203,4205],{"className":4204},[1896],[1898,4206,4207],{"xmlns":1900},[1902,4208,4209,4217],{},[1905,4210,4211],{},[1963,4212,4213,4215],{},[1908,4214,1910],{},[1969,4216,1971],{},[1912,4218,4219],{"encoding":1914},"L_1",[1889,4221,4223],{"className":4222,"ariaHidden":1919},[1918],[1889,4224,4226,4229],{"className":4225},[1923],[1889,4227],{"className":4228,"style":3229},[1927],[1889,4230,4232,4235],{"className":4231},[1932],[1889,4233,1910],{"className":4234},[1932,1933],[1889,4236,4238],{"className":4237},[2071],[1889,4239,4241,4261],{"className":4240},[2075,2076],[1889,4242,4244,4258],{"className":4243},[2080],[1889,4245,4247],{"className":4246,"style":2085},[2084],[1889,4248,4249,4252],{"style":2088},[1889,4250],{"className":4251,"style":2093},[2092],[1889,4253,4255],{"className":4254},[2097,2098,2099,2100],[1889,4256,1971],{"className":4257},[1932,2100],[1889,4259,2108],{"className":4260},[2107],[1889,4262,4264],{"className":4263},[2080],[1889,4265,4267],{"className":4266,"style":2115},[2084],[1889,4268],{},[1889,4270,4272,4290],{"className":4271},[1892],[1889,4273,4275],{"className":4274},[1896],[1898,4276,4277],{"xmlns":1900},[1902,4278,4279,4287],{},[1905,4280,4281],{},[1963,4282,4283,4285],{},[1908,4284,1910],{},[1969,4286,3352],{},[1912,4288,4289],{"encoding":1914},"L_3",[1889,4291,4293],{"className":4292,"ariaHidden":1919},[1918],[1889,4294,4296,4299],{"className":4295},[1923],[1889,4297],{"className":4298,"style":3229},[1927],[1889,4300,4302,4305],{"className":4301},[1932],[1889,4303,1910],{"className":4304},[1932,1933],[1889,4306,4308],{"className":4307},[2071],[1889,4309,4311,4331],{"className":4310},[2075,2076],[1889,4312,4314,4328],{"className":4313},[2080],[1889,4315,4317],{"className":4316,"style":2085},[2084],[1889,4318,4319,4322],{"style":2088},[1889,4320],{"className":4321,"style":2093},[2092],[1889,4323,4325],{"className":4324},[2097,2098,2099,2100],[1889,4326,3352],{"className":4327},[1932,2100],[1889,4329,2108],{"className":4330},[2107],[1889,4332,4334],{"className":4333},[2080],[1889,4335,4337],{"className":4336,"style":2115},[2084],[1889,4338],{},"之间，那么一定存在某个混合彩票（部分概率得到",[1889,4341,4343,4360],{"className":4342},[1892],[1889,4344,4346],{"className":4345},[1896],[1898,4347,4348],{"xmlns":1900},[1902,4349,4350,4358],{},[1905,4351,4352],{},[1963,4353,4354,4356],{},[1908,4355,1910],{},[1969,4357,1971],{},[1912,4359,4219],{"encoding":1914},[1889,4361,4363],{"className":4362,"ariaHidden":1919},[1918],[1889,4364,4366,4369],{"className":4365},[1923],[1889,4367],{"className":4368,"style":3229},[1927],[1889,4370,4372,4375],{"className":4371},[1932],[1889,4373,1910],{"className":4374},[1932,1933],[1889,4376,4378],{"className":4377},[2071],[1889,4379,4381,4401],{"className":4380},[2075,2076],[1889,4382,4384,4398],{"className":4383},[2080],[1889,4385,4387],{"className":4386,"style":2085},[2084],[1889,4388,4389,4392],{"style":2088},[1889,4390],{"className":4391,"style":2093},[2092],[1889,4393,4395],{"className":4394},[2097,2098,2099,2100],[1889,4396,1971],{"className":4397},[1932,2100],[1889,4399,2108],{"className":4400},[2107],[1889,4402,4404],{"className":4403},[2080],[1889,4405,4407],{"className":4406,"style":2115},[2084],[1889,4408],{},"，部分概率得到",[1889,4411,4413,4430],{"className":4412},[1892],[1889,4414,4416],{"className":4415},[1896],[1898,4417,4418],{"xmlns":1900},[1902,4419,4420,4428],{},[1905,4421,4422],{},[1963,4423,4424,4426],{},[1908,4425,1910],{},[1969,4427,3352],{},[1912,4429,4289],{"encoding":1914},[1889,4431,4433],{"className":4432,"ariaHidden":1919},[1918],[1889,4434,4436,4439],{"className":4435},[1923],[1889,4437],{"className":4438,"style":3229},[1927],[1889,4440,4442,4445],{"className":4441},[1932],[1889,4443,1910],{"className":4444},[1932,1933],[1889,4446,4448],{"className":4447},[2071],[1889,4449,4451,4471],{"className":4450},[2075,2076],[1889,4452,4454,4468],{"className":4453},[2080],[1889,4455,4457],{"className":4456,"style":2085},[2084],[1889,4458,4459,4462],{"style":2088},[1889,4460],{"className":4461,"style":2093},[2092],[1889,4463,4465],{"className":4464},[2097,2098,2099,2100],[1889,4466,3352],{"className":4467},[1932,2100],[1889,4469,2108],{"className":4470},[2107],[1889,4472,4474],{"className":4473},[2080],[1889,4475,4477],{"className":4476,"style":2115},[2084],[1889,4478],{},"）与",[1889,4481,4483,4500],{"className":4482},[1892],[1889,4484,4486],{"className":4485},[1896],[1898,4487,4488],{"xmlns":1900},[1902,4489,4490,4498],{},[1905,4491,4492],{},[1963,4493,4494,4496],{},[1908,4495,1910],{},[1969,4497,1990],{},[1912,4499,4148],{"encoding":1914},[1889,4501,4503],{"className":4502,"ariaHidden":1919},[1918],[1889,4504,4506,4509],{"className":4505},[1923],[1889,4507],{"className":4508,"style":3229},[1927],[1889,4510,4512,4515],{"className":4511},[1932],[1889,4513,1910],{"className":4514},[1932,1933],[1889,4516,4518],{"className":4517},[2071],[1889,4519,4521,4541],{"className":4520},[2075,2076],[1889,4522,4524,4538],{"className":4523},[2080],[1889,4525,4527],{"className":4526,"style":2085},[2084],[1889,4528,4529,4532],{"style":2088},[1889,4530],{"className":4531,"style":2093},[2092],[1889,4533,4535],{"className":4534},[2097,2098,2099,2100],[1889,4536,1990],{"className":4537},[1932,2100],[1889,4539,2108],{"className":4540},[2107],[1889,4542,4544],{"className":4543},[2080],[1889,4545,4547],{"className":4546,"style":2115},[2084],[1889,4548],{},"无差异。",[1798,4551,4552,3190,4555,4688,4689,2769,4758,4831],{},[1884,4553,4554],{},"公理4: 独立性 (Independence)",[1889,4556,4558,4584],{"className":4557},[1892],[1889,4559,4561],{"className":4560},[1896],[1898,4562,4563],{"xmlns":1900},[1902,4564,4565,4581],{},[1905,4566,4567,4573,4575],{},[1963,4568,4569,4571],{},[1908,4570,1910],{},[1969,4572,1971],{},[1955,4574,2985],{},[1963,4576,4577,4579],{},[1908,4578,1910],{},[1969,4580,1990],{},[1912,4582,4583],{"encoding":1914},"L_1 \\sim L_2",[1889,4585,4587,4642],{"className":4586,"ariaHidden":1919},[1918],[1889,4588,4590,4593,4633,4636,4639],{"className":4589},[1923],[1889,4591],{"className":4592,"style":3229},[1927],[1889,4594,4596,4599],{"className":4595},[1932],[1889,4597,1910],{"className":4598},[1932,1933],[1889,4600,4602],{"className":4601},[2071],[1889,4603,4605,4625],{"className":4604},[2075,2076],[1889,4606,4608,4622],{"className":4607},[2080],[1889,4609,4611],{"className":4610,"style":2085},[2084],[1889,4612,4613,4616],{"style":2088},[1889,4614],{"className":4615,"style":2093},[2092],[1889,4617,4619],{"className":4618},[2097,2098,2099,2100],[1889,4620,1971],{"className":4621},[1932,2100],[1889,4623,2108],{"className":4624},[2107],[1889,4626,4628],{"className":4627},[2080],[1889,4629,4631],{"className":4630,"style":2115},[2084],[1889,4632],{},[1889,4634],{"className":4635,"style":2043},[2042],[1889,4637,2985],{"className":4638},[2047],[1889,4640],{"className":4641,"style":2043},[2042],[1889,4643,4645,4648],{"className":4644},[1923],[1889,4646],{"className":4647,"style":3229},[1927],[1889,4649,4651,4654],{"className":4650},[1932],[1889,4652,1910],{"className":4653},[1932,1933],[1889,4655,4657],{"className":4656},[2071],[1889,4658,4660,4680],{"className":4659},[2075,2076],[1889,4661,4663,4677],{"className":4662},[2080],[1889,4664,4666],{"className":4665,"style":2085},[2084],[1889,4667,4668,4671],{"style":2088},[1889,4669],{"className":4670,"style":2093},[2092],[1889,4672,4674],{"className":4673},[2097,2098,2099,2100],[1889,4675,1990],{"className":4676},[1932,2100],[1889,4678,2108],{"className":4679},[2107],[1889,4681,4683],{"className":4682},[2080],[1889,4684,4686],{"className":4685,"style":2115},[2084],[1889,4687],{},"，那么对于任何",[1889,4690,4692,4709],{"className":4691},[1892],[1889,4693,4695],{"className":4694},[1896],[1898,4696,4697],{"xmlns":1900},[1902,4698,4699,4707],{},[1905,4700,4701],{},[1963,4702,4703,4705],{},[1908,4704,1910],{},[1969,4706,3352],{},[1912,4708,4289],{"encoding":1914},[1889,4710,4712],{"className":4711,"ariaHidden":1919},[1918],[1889,4713,4715,4718],{"className":4714},[1923],[1889,4716],{"className":4717,"style":3229},[1927],[1889,4719,4721,4724],{"className":4720},[1932],[1889,4722,1910],{"className":4723},[1932,1933],[1889,4725,4727],{"className":4726},[2071],[1889,4728,4730,4750],{"className":4729},[2075,2076],[1889,4731,4733,4747],{"className":4732},[2080],[1889,4734,4736],{"className":4735,"style":2085},[2084],[1889,4737,4738,4741],{"style":2088},[1889,4739],{"className":4740,"style":2093},[2092],[1889,4742,4744],{"className":4743},[2097,2098,2099,2100],[1889,4745,3352],{"className":4746},[1932,2100],[1889,4748,2108],{"className":4749},[2107],[1889,4751,4753],{"className":4752},[2080],[1889,4754,4756],{"className":4755,"style":2115},[2084],[1889,4757],{},[1889,4759,4761,4786],{"className":4760},[1892],[1889,4762,4764],{"className":4763},[1896],[1898,4765,4766],{"xmlns":1900},[1902,4767,4768,4784],{},[1905,4769,4770,4772,4774,4776,4778,4780,4782],{},[1908,4771,3811],{},[1955,4773,3814],{},[1955,4775,1961],{"stretchy":1960},[1969,4777,3819],{},[1955,4779,1974],{"separator":1919},[1969,4781,1971],{},[1955,4783,2023],{"stretchy":1960},[1912,4785,3828],{"encoding":1914},[1889,4787,4789,4807],{"className":4788,"ariaHidden":1919},[1918],[1889,4790,4792,4795,4798,4801,4804],{"className":4791},[1923],[1889,4793],{"className":4794,"style":3838},[1927],[1889,4796,3811],{"className":4797,"style":3842},[1932,1933],[1889,4799],{"className":4800,"style":2043},[2042],[1889,4802,3814],{"className":4803},[2047],[1889,4805],{"className":4806,"style":2043},[2042],[1889,4808,4810,4813,4816,4819,4822,4825,4828],{"className":4809},[1923],[1889,4811],{"className":4812,"style":2057},[1927],[1889,4814,1961],{"className":4815},[2061],[1889,4817,3819],{"className":4818},[1932],[1889,4820,1974],{"className":4821},[2121],[1889,4823],{"className":4824,"style":2125},[2042],[1889,4826,1971],{"className":4827},[1932],[1889,4829,2023],{"className":4830},[2367],"：",[1889,4833,4835],{"className":4834},[1938],[1889,4836,4838,4904],{"className":4837},[1892],[1889,4839,4841],{"className":4840},[1896],[1898,4842,4843],{"xmlns":1900,"display":1947},[1902,4844,4845,4901],{},[1905,4846,4847,4849,4855,4857,4859,4861,4863,4865,4867,4873,4875,4877,4883,4885,4887,4889,4891,4893,4895],{},[1908,4848,3811],{},[1963,4850,4851,4853],{},[1908,4852,1910],{},[1969,4854,1971],{},[1955,4856,3910],{},[1955,4858,1961],{"stretchy":1960},[1969,4860,1971],{},[1955,4862,3917],{},[1908,4864,3811],{},[1955,4866,2023],{"stretchy":1960},[1963,4868,4869,4871],{},[1908,4870,1910],{},[1969,4872,3352],{},[1955,4874,2985],{},[1908,4876,3811],{},[1963,4878,4879,4881],{},[1908,4880,1910],{},[1969,4882,1990],{},[1955,4884,3910],{},[1955,4886,1961],{"stretchy":1960},[1969,4888,1971],{},[1955,4890,3917],{},[1908,4892,3811],{},[1955,4894,2023],{"stretchy":1960},[1963,4896,4897,4899],{},[1908,4898,1910],{},[1969,4900,3352],{},[1912,4902,4903],{"encoding":1914},"\\alpha L_1 + (1-\\alpha) L_3 \\sim \\alpha L_2 + (1-\\alpha) L_3",[1889,4905,4907,4965,4986,5047,5105,5126],{"className":4906,"ariaHidden":1919},[1918],[1889,4908,4910,4913,4916,4956,4959,4962],{"className":4909},[1923],[1889,4911],{"className":4912,"style":3229},[1927],[1889,4914,3811],{"className":4915,"style":3842},[1932,1933],[1889,4917,4919,4922],{"className":4918},[1932],[1889,4920,1910],{"className":4921},[1932,1933],[1889,4923,4925],{"className":4924},[2071],[1889,4926,4928,4948],{"className":4927},[2075,2076],[1889,4929,4931,4945],{"className":4930},[2080],[1889,4932,4934],{"className":4933,"style":2085},[2084],[1889,4935,4936,4939],{"style":2088},[1889,4937],{"className":4938,"style":2093},[2092],[1889,4940,4942],{"className":4941},[2097,2098,2099,2100],[1889,4943,1971],{"className":4944},[1932,2100],[1889,4946,2108],{"className":4947},[2107],[1889,4949,4951],{"className":4950},[2080],[1889,4952,4954],{"className":4953,"style":2115},[2084],[1889,4955],{},[1889,4957],{"className":4958,"style":4041},[2042],[1889,4960,3910],{"className":4961},[4045],[1889,4963],{"className":4964,"style":4041},[2042],[1889,4966,4968,4971,4974,4977,4980,4983],{"className":4967},[1923],[1889,4969],{"className":4970,"style":2057},[1927],[1889,4972,1961],{"className":4973},[2061],[1889,4975,1971],{"className":4976},[1932],[1889,4978],{"className":4979,"style":4041},[2042],[1889,4981,3917],{"className":4982},[4045],[1889,4984],{"className":4985,"style":4041},[2042],[1889,4987,4989,4992,4995,4998,5038,5041,5044],{"className":4988},[1923],[1889,4990],{"className":4991,"style":2057},[1927],[1889,4993,3811],{"className":4994,"style":3842},[1932,1933],[1889,4996,2023],{"className":4997},[2367],[1889,4999,5001,5004],{"className":5000},[1932],[1889,5002,1910],{"className":5003},[1932,1933],[1889,5005,5007],{"className":5006},[2071],[1889,5008,5010,5030],{"className":5009},[2075,2076],[1889,5011,5013,5027],{"className":5012},[2080],[1889,5014,5016],{"className":5015,"style":2085},[2084],[1889,5017,5018,5021],{"style":2088},[1889,5019],{"className":5020,"style":2093},[2092],[1889,5022,5024],{"className":5023},[2097,2098,2099,2100],[1889,5025,3352],{"className":5026},[1932,2100],[1889,5028,2108],{"className":5029},[2107],[1889,5031,5033],{"className":5032},[2080],[1889,5034,5036],{"className":5035,"style":2115},[2084],[1889,5037],{},[1889,5039],{"className":5040,"style":2043},[2042],[1889,5042,2985],{"className":5043},[2047],[1889,5045],{"className":5046,"style":2043},[2042],[1889,5048,5050,5053,5056,5096,5099,5102],{"className":5049},[1923],[1889,5051],{"className":5052,"style":3229},[1927],[1889,5054,3811],{"className":5055,"style":3842},[1932,1933],[1889,5057,5059,5062],{"className":5058},[1932],[1889,5060,1910],{"className":5061},[1932,1933],[1889,5063,5065],{"className":5064},[2071],[1889,5066,5068,5088],{"className":5067},[2075,2076],[1889,5069,5071,5085],{"className":5070},[2080],[1889,5072,5074],{"className":5073,"style":2085},[2084],[1889,5075,5076,5079],{"style":2088},[1889,5077],{"className":5078,"style":2093},[2092],[1889,5080,5082],{"className":5081},[2097,2098,2099,2100],[1889,5083,1990],{"className":5084},[1932,2100],[1889,5086,2108],{"className":5087},[2107],[1889,5089,5091],{"className":5090},[2080],[1889,5092,5094],{"className":5093,"style":2115},[2084],[1889,5095],{},[1889,5097],{"className":5098,"style":4041},[2042],[1889,5100,3910],{"className":5101},[4045],[1889,5103],{"className":5104,"style":4041},[2042],[1889,5106,5108,5111,5114,5117,5120,5123],{"className":5107},[1923],[1889,5109],{"className":5110,"style":2057},[1927],[1889,5112,1961],{"className":5113},[2061],[1889,5115,1971],{"className":5116},[1932],[1889,5118],{"className":5119,"style":4041},[2042],[1889,5121,3917],{"className":5122},[4045],[1889,5124],{"className":5125,"style":4041},[2042],[1889,5127,5129,5132,5135,5138],{"className":5128},[1923],[1889,5130],{"className":5131,"style":2057},[1927],[1889,5133,3811],{"className":5134,"style":3842},[1932,1933],[1889,5136,2023],{"className":5137},[2367],[1889,5139,5141,5144],{"className":5140},[1932],[1889,5142,1910],{"className":5143},[1932,1933],[1889,5145,5147],{"className":5146},[2071],[1889,5148,5150,5170],{"className":5149},[2075,2076],[1889,5151,5153,5167],{"className":5152},[2080],[1889,5154,5156],{"className":5155,"style":2085},[2084],[1889,5157,5158,5161],{"style":2088},[1889,5159],{"className":5160,"style":2093},[2092],[1889,5162,5164],{"className":5163},[2097,2098,2099,2100],[1889,5165,3352],{"className":5166},[1932,2100],[1889,5168,2108],{"className":5169},[2107],[1889,5171,5173],{"className":5172},[2080],[1889,5174,5176],{"className":5175,"style":2115},[2084],[1889,5177],{},[1798,5179,5180,5182,5183,5252],{},[1884,5181,4126],{},": 在两个彩票中加入相同的\"噪音\"",[1889,5184,5186,5203],{"className":5185},[1892],[1889,5187,5189],{"className":5188},[1896],[1898,5190,5191],{"xmlns":1900},[1902,5192,5193,5201],{},[1905,5194,5195],{},[1963,5196,5197,5199],{},[1908,5198,1910],{},[1969,5200,3352],{},[1912,5202,4289],{"encoding":1914},[1889,5204,5206],{"className":5205,"ariaHidden":1919},[1918],[1889,5207,5209,5212],{"className":5208},[1923],[1889,5210],{"className":5211,"style":3229},[1927],[1889,5213,5215,5218],{"className":5214},[1932],[1889,5216,1910],{"className":5217},[1932,1933],[1889,5219,5221],{"className":5220},[2071],[1889,5222,5224,5244],{"className":5223},[2075,2076],[1889,5225,5227,5241],{"className":5226},[2080],[1889,5228,5230],{"className":5229,"style":2085},[2084],[1889,5231,5232,5235],{"style":2088},[1889,5233],{"className":5234,"style":2093},[2092],[1889,5236,5238],{"className":5237},[2097,2098,2099,2100],[1889,5239,3352],{"className":5240},[1932,2100],[1889,5242,2108],{"className":5243},[2107],[1889,5245,5247],{"className":5246},[2080],[1889,5248,5250],{"className":5249,"style":2115},[2084],[1889,5251],{},"不应该改变偏好顺序。这是期望效用理论最有争议的公理。",[1877,5254,5256],{"id":5255},"_13-期望效用定理","1.3 期望效用定理",[1798,5258,5259,5262,5263,5293,5294,5374,5375,5655],{},[1884,5260,5261],{},"定理 (vNM, 1944)",": 如果偏好",[1889,5264,5266,5280],{"className":5265},[1892],[1889,5267,5269],{"className":5268},[1896],[1898,5270,5271],{"xmlns":1900},[1902,5272,5273,5277],{},[1905,5274,5275],{},[1955,5276,2949],{},[1912,5278,5279],{"encoding":1914},"\\succeq",[1889,5281,5283],{"className":5282,"ariaHidden":1919},[1918],[1889,5284,5286,5290],{"className":5285},[1923],[1889,5287],{"className":5288,"style":5289},[1927],"height:0.7719em;vertical-align:-0.136em;",[1889,5291,2949],{"className":5292},[2047],"满足上述四个公理，那么存在效用函数",[1889,5295,5297,5323],{"className":5296},[1892],[1889,5298,5300],{"className":5299},[1896],[1898,5301,5302],{"xmlns":1900},[1902,5303,5304,5320],{},[1905,5305,5306,5309,5311,5315,5318],{},[1908,5307,5308],{},"u",[1955,5310,2704],{},[1908,5312,5314],{"mathvariant":5313},"double-struck","R",[1955,5316,5317],{},"→",[1908,5319,5314],{"mathvariant":5313},[1912,5321,5322],{"encoding":1914},"u: \\mathbb{R} \\to \\mathbb{R}",[1889,5324,5326,5345,5365],{"className":5325,"ariaHidden":1919},[1918],[1889,5327,5329,5333,5336,5339,5342],{"className":5328},[1923],[1889,5330],{"className":5331,"style":5332},[1927],"height:0.4306em;",[1889,5334,5308],{"className":5335},[1932,1933],[1889,5337],{"className":5338,"style":2043},[2042],[1889,5340,2704],{"className":5341},[2047],[1889,5343],{"className":5344,"style":2043},[2042],[1889,5346,5348,5352,5356,5359,5362],{"className":5347},[1923],[1889,5349],{"className":5350,"style":5351},[1927],"height:0.6889em;",[1889,5353,5314],{"className":5354},[1932,5355],"mathbb",[1889,5357],{"className":5358,"style":2043},[2042],[1889,5360,5317],{"className":5361},[2047],[1889,5363],{"className":5364,"style":2043},[2042],[1889,5366,5368,5371],{"className":5367},[1923],[1889,5369],{"className":5370,"style":5351},[1927],[1889,5372,5314],{"className":5373},[1932,5355],"，使得彩票",[1889,5376,5378,5432],{"className":5377},[1892],[1889,5379,5381],{"className":5380},[1896],[1898,5382,5383],{"xmlns":1900},[1902,5384,5385,5429],{},[1905,5386,5387,5389,5391,5393,5399,5401,5407,5409,5411,5413,5419,5421,5427],{},[1908,5388,1910],{},[1955,5390,1957],{},[1955,5392,1961],{"stretchy":1960},[1963,5394,5395,5397],{},[1908,5396,1967],{},[1969,5398,1971],{},[1955,5400,1974],{"separator":1919},[1963,5402,5403,5405],{},[1908,5404,1798],{},[1969,5406,1971],{},[1955,5408,1983],{"separator":1919},[1955,5410,2003],{},[1955,5412,1983],{"separator":1919},[1963,5414,5415,5417],{},[1908,5416,1967],{},[1908,5418,2012],{},[1955,5420,1974],{"separator":1919},[1963,5422,5423,5425],{},[1908,5424,1798],{},[1908,5426,2012],{},[1955,5428,2023],{"stretchy":1960},[1912,5430,5431],{"encoding":1914},"L = (x_1, p_1; \\ldots; x_n, p_n)",[1889,5433,5435,5453],{"className":5434,"ariaHidden":1919},[1918],[1889,5436,5438,5441,5444,5447,5450],{"className":5437},[1923],[1889,5439],{"className":5440,"style":1928},[1927],[1889,5442,1910],{"className":5443},[1932,1933],[1889,5445],{"className":5446,"style":2043},[2042],[1889,5448,1957],{"className":5449},[2047],[1889,5451],{"className":5452,"style":2043},[2042],[1889,5454,5456,5459,5462,5502,5505,5508,5548,5551,5554,5557,5560,5563,5566,5606,5609,5612,5652],{"className":5455},[1923],[1889,5457],{"className":5458,"style":2057},[1927],[1889,5460,1961],{"className":5461},[2061],[1889,5463,5465,5468],{"className":5464},[1932],[1889,5466,1967],{"className":5467},[1932,1933],[1889,5469,5471],{"className":5470},[2071],[1889,5472,5474,5494],{"className":5473},[2075,2076],[1889,5475,5477,5491],{"className":5476},[2080],[1889,5478,5480],{"className":5479,"style":2085},[2084],[1889,5481,5482,5485],{"style":2088},[1889,5483],{"className":5484,"style":2093},[2092],[1889,5486,5488],{"className":5487},[2097,2098,2099,2100],[1889,5489,1971],{"className":5490},[1932,2100],[1889,5492,2108],{"className":5493},[2107],[1889,5495,5497],{"className":5496},[2080],[1889,5498,5500],{"className":5499,"style":2115},[2084],[1889,5501],{},[1889,5503,1974],{"className":5504},[2121],[1889,5506],{"className":5507,"style":2125},[2042],[1889,5509,5511,5514],{"className":5510},[1932],[1889,5512,1798],{"className":5513},[1932,1933],[1889,5515,5517],{"className":5516},[2071],[1889,5518,5520,5540],{"className":5519},[2075,2076],[1889,5521,5523,5537],{"className":5522},[2080],[1889,5524,5526],{"className":5525,"style":2085},[2084],[1889,5527,5528,5531],{"style":2088},[1889,5529],{"className":5530,"style":2093},[2092],[1889,5532,5534],{"className":5533},[2097,2098,2099,2100],[1889,5535,1971],{"className":5536},[1932,2100],[1889,5538,2108],{"className":5539},[2107],[1889,5541,5543],{"className":5542},[2080],[1889,5544,5546],{"className":5545,"style":2115},[2084],[1889,5547],{},[1889,5549,1983],{"className":5550},[2121],[1889,5552],{"className":5553,"style":2125},[2042],[1889,5555,2003],{"className":5556},[2267],[1889,5558],{"className":5559,"style":2125},[2042],[1889,5561,1983],{"className":5562},[2121],[1889,5564],{"className":5565,"style":2125},[2042],[1889,5567,5569,5572],{"className":5568},[1932],[1889,5570,1967],{"className":5571},[1932,1933],[1889,5573,5575],{"className":5574},[2071],[1889,5576,5578,5598],{"className":5577},[2075,2076],[1889,5579,5581,5595],{"className":5580},[2080],[1889,5582,5584],{"className":5583,"style":2295},[2084],[1889,5585,5586,5589],{"style":2088},[1889,5587],{"className":5588,"style":2093},[2092],[1889,5590,5592],{"className":5591},[2097,2098,2099,2100],[1889,5593,2012],{"className":5594},[1932,1933,2100],[1889,5596,2108],{"className":5597},[2107],[1889,5599,5601],{"className":5600},[2080],[1889,5602,5604],{"className":5603,"style":2115},[2084],[1889,5605],{},[1889,5607,1974],{"className":5608},[2121],[1889,5610],{"className":5611,"style":2125},[2042],[1889,5613,5615,5618],{"className":5614},[1932],[1889,5616,1798],{"className":5617},[1932,1933],[1889,5619,5621],{"className":5620},[2071],[1889,5622,5624,5644],{"className":5623},[2075,2076],[1889,5625,5627,5641],{"className":5626},[2080],[1889,5628,5630],{"className":5629,"style":2295},[2084],[1889,5631,5632,5635],{"style":2088},[1889,5633],{"className":5634,"style":2093},[2092],[1889,5636,5638],{"className":5637},[2097,2098,2099,2100],[1889,5639,2012],{"className":5640},[1932,1933,2100],[1889,5642,2108],{"className":5643},[2107],[1889,5645,5647],{"className":5646},[2080],[1889,5648,5650],{"className":5649,"style":2115},[2084],[1889,5651],{},[1889,5653,2023],{"className":5654},[2367],"的评价为：",[1889,5657,5659],{"className":5658},[1938],[1889,5660,5662,5737],{"className":5661},[1892],[1889,5663,5665],{"className":5664},[1896],[1898,5666,5667],{"xmlns":1900,"display":1947},[1902,5668,5669,5734],{},[1905,5670,5671,5674,5676,5678,5680,5682,5697,5703,5705,5707,5713,5715,5717,5720,5723,5725,5727,5729,5731],{},[1908,5672,5673],{},"U",[1955,5675,1961],{"stretchy":1960},[1908,5677,1910],{},[1955,5679,2023],{"stretchy":1960},[1955,5681,1957],{},[5683,5684,5685,5687,5695],"munderover",{},[1955,5686,2534],{},[1905,5688,5689,5691,5693],{},[1908,5690,2389],{},[1955,5692,1957],{},[1969,5694,1971],{},[1908,5696,2012],{},[1963,5698,5699,5701],{},[1908,5700,1798],{},[1908,5702,2389],{},[1908,5704,5308],{},[1955,5706,1961],{"stretchy":1960},[1963,5708,5709,5711],{},[1908,5710,1967],{},[1908,5712,2389],{},[1955,5714,2023],{"stretchy":1960},[1955,5716,1957],{},[1908,5718,5719],{"mathvariant":5313},"E",[1955,5721,5722],{"stretchy":1960},"[",[1908,5724,5308],{},[1955,5726,1961],{"stretchy":1960},[1908,5728,1967],{},[1955,5730,2023],{"stretchy":1960},[1955,5732,5733],{"stretchy":1960},"]",[1912,5735,5736],{"encoding":1914},"U(L) = \\sum_{i=1}^n p_i u(x_i) = \\mathbb{E}[u(x)]",[1889,5738,5740,5768,5948],{"className":5739,"ariaHidden":1919},[1918],[1889,5741,5743,5746,5750,5753,5756,5759,5762,5765],{"className":5742},[1923],[1889,5744],{"className":5745,"style":2057},[1927],[1889,5747,5673],{"className":5748,"style":5749},[1932,1933],"margin-right:0.109em;",[1889,5751,1961],{"className":5752},[2061],[1889,5754,1910],{"className":5755},[1932,1933],[1889,5757,2023],{"className":5758},[2367],[1889,5760],{"className":5761,"style":2043},[2042],[1889,5763,1957],{"className":5764},[2047],[1889,5766],{"className":5767,"style":2043},[2042],[1889,5769,5771,5775,5847,5850,5890,5893,5896,5936,5939,5942,5945],{"className":5770},[1923],[1889,5772],{"className":5773,"style":5774},[1927],"height:2.9291em;vertical-align:-1.2777em;",[1889,5776,5779],{"className":5777},[2571,5778],"op-limits",[1889,5780,5782,5838],{"className":5781},[2075,2076],[1889,5783,5785,5835],{"className":5784},[2080],[1889,5786,5789,5811,5823],{"className":5787,"style":5788},[2084],"height:1.6514em;",[1889,5790,5792,5796],{"style":5791},"top:-1.8723em;margin-left:0em;",[1889,5793],{"className":5794,"style":5795},[2092],"height:3.05em;",[1889,5797,5799],{"className":5798},[2097,2098,2099,2100],[1889,5800,5802,5805,5808],{"className":5801},[1932,2100],[1889,5803,2389],{"className":5804},[1932,1933,2100],[1889,5806,1957],{"className":5807},[2047,2100],[1889,5809,1971],{"className":5810},[1932,2100],[1889,5812,5814,5817],{"style":5813},"top:-3.05em;",[1889,5815],{"className":5816,"style":5795},[2092],[1889,5818,5819],{},[1889,5820,2534],{"className":5821},[2571,2575,5822],"large-op",[1889,5824,5826,5829],{"style":5825},"top:-4.3em;margin-left:0em;",[1889,5827],{"className":5828,"style":5795},[2092],[1889,5830,5832],{"className":5831},[2097,2098,2099,2100],[1889,5833,2012],{"className":5834},[1932,1933,2100],[1889,5836,2108],{"className":5837},[2107],[1889,5839,5841],{"className":5840},[2080],[1889,5842,5845],{"className":5843,"style":5844},[2084],"height:1.2777em;",[1889,5846],{},[1889,5848],{"className":5849,"style":2125},[2042],[1889,5851,5853,5856],{"className":5852},[1932],[1889,5854,1798],{"className":5855},[1932,1933],[1889,5857,5859],{"className":5858},[2071],[1889,5860,5862,5882],{"className":5861},[2075,2076],[1889,5863,5865,5879],{"className":5864},[2080],[1889,5866,5868],{"className":5867,"style":2421},[2084],[1889,5869,5870,5873],{"style":2088},[1889,5871],{"className":5872,"style":2093},[2092],[1889,5874,5876],{"className":5875},[2097,2098,2099,2100],[1889,5877,2389],{"className":5878},[1932,1933,2100],[1889,5880,2108],{"className":5881},[2107],[1889,5883,5885],{"className":5884},[2080],[1889,5886,5888],{"className":5887,"style":2115},[2084],[1889,5889],{},[1889,5891,5308],{"className":5892},[1932,1933],[1889,5894,1961],{"className":5895},[2061],[1889,5897,5899,5902],{"className":5898},[1932],[1889,5900,1967],{"className":5901},[1932,1933],[1889,5903,5905],{"className":5904},[2071],[1889,5906,5908,5928],{"className":5907},[2075,2076],[1889,5909,5911,5925],{"className":5910},[2080],[1889,5912,5914],{"className":5913,"style":2421},[2084],[1889,5915,5916,5919],{"style":2088},[1889,5917],{"className":5918,"style":2093},[2092],[1889,5920,5922],{"className":5921},[2097,2098,2099,2100],[1889,5923,2389],{"className":5924},[1932,1933,2100],[1889,5926,2108],{"className":5927},[2107],[1889,5929,5931],{"className":5930},[2080],[1889,5932,5934],{"className":5933,"style":2115},[2084],[1889,5935],{},[1889,5937,2023],{"className":5938},[2367],[1889,5940],{"className":5941,"style":2043},[2042],[1889,5943,1957],{"className":5944},[2047],[1889,5946],{"className":5947,"style":2043},[2042],[1889,5949,5951,5954,5957,5960,5963,5966,5969],{"className":5950},[1923],[1889,5952],{"className":5953,"style":2057},[1927],[1889,5955,5719],{"className":5956},[1932,5355],[1889,5958,5722],{"className":5959},[2061],[1889,5961,5308],{"className":5962},[1932,1933],[1889,5964,1961],{"className":5965},[2061],[1889,5967,1967],{"className":5968},[1932,1933],[1889,5970,5972],{"className":5971},[2367],")]",[1798,5974,3325,5975,6059,6060,2698],{},[1889,5976,5978,6000],{"className":5977},[1892],[1889,5979,5981],{"className":5980},[1896],[1898,5982,5983],{"xmlns":1900},[1902,5984,5985,5997],{},[1905,5986,5987,5989,5991],{},[1908,5988,1910],{},[1955,5990,2949],{},[2783,5992,5993,5995],{},[1908,5994,1910],{},[1955,5996,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1912,5998,5999],{"encoding":1914},"L \\succeq L'",[1889,6001,6003,6021],{"className":6002,"ariaHidden":1919},[1918],[1889,6004,6006,6009,6012,6015,6018],{"className":6005},[1923],[1889,6007],{"className":6008,"style":3004},[1927],[1889,6010,1910],{"className":6011},[1932,1933],[1889,6013],{"className":6014,"style":2043},[2042],[1889,6016,2949],{"className":6017},[2047],[1889,6019],{"className":6020,"style":2043},[2042],[1889,6022,6024,6027],{"className":6023},[1923],[1889,6025],{"className":6026,"style":2804},[1927],[1889,6028,6030,6033],{"className":6029},[1932],[1889,6031,1910],{"className":6032},[1932,1933],[1889,6034,6036],{"className":6035},[2071],[1889,6037,6039],{"className":6038},[2075],[1889,6040,6042],{"className":6041},[2080],[1889,6043,6045],{"className":6044,"style":2804},[2084],[1889,6046,6047,6050],{"style":2825},[1889,6048],{"className":6049,"style":2093},[2092],[1889,6051,6053],{"className":6052},[2097,2098,2099,2100],[1889,6054,6056],{"className":6055},[1932,2100],[1889,6057,2791],{"className":6058},[1932,2100],"当且仅当",[1889,6061,6063,6098],{"className":6062},[1892],[1889,6064,6066],{"className":6065},[1896],[1898,6067,6068],{"xmlns":1900},[1902,6069,6070,6095],{},[1905,6071,6072,6074,6076,6078,6080,6083,6085,6087,6093],{},[1908,6073,5673],{},[1955,6075,1961],{"stretchy":1960},[1908,6077,1910],{},[1955,6079,2023],{"stretchy":1960},[1955,6081,6082],{},"≥",[1908,6084,5673],{},[1955,6086,1961],{"stretchy":1960},[2783,6088,6089,6091],{},[1908,6090,1910],{},[1955,6092,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,6094,2023],{"stretchy":1960},[1912,6096,6097],{"encoding":1914},"U(L) \\ge U(L')",[1889,6099,6101,6128],{"className":6100,"ariaHidden":1919},[1918],[1889,6102,6104,6107,6110,6113,6116,6119,6122,6125],{"className":6103},[1923],[1889,6105],{"className":6106,"style":2057},[1927],[1889,6108,5673],{"className":6109,"style":5749},[1932,1933],[1889,6111,1961],{"className":6112},[2061],[1889,6114,1910],{"className":6115},[1932,1933],[1889,6117,2023],{"className":6118},[2367],[1889,6120],{"className":6121,"style":2043},[2042],[1889,6123,6082],{"className":6124},[2047],[1889,6126],{"className":6127,"style":2043},[2042],[1889,6129,6131,6135,6138,6141,6173],{"className":6130},[1923],[1889,6132],{"className":6133,"style":6134},[1927],"height:1.0019em;vertical-align:-0.25em;",[1889,6136,5673],{"className":6137,"style":5749},[1932,1933],[1889,6139,1961],{"className":6140},[2061],[1889,6142,6144,6147],{"className":6143},[1932],[1889,6145,1910],{"className":6146},[1932,1933],[1889,6148,6150],{"className":6149},[2071],[1889,6151,6153],{"className":6152},[2075],[1889,6154,6156],{"className":6155},[2080],[1889,6157,6159],{"className":6158,"style":2804},[2084],[1889,6160,6161,6164],{"style":2825},[1889,6162],{"className":6163,"style":2093},[2092],[1889,6165,6167],{"className":6166},[2097,2098,2099,2100],[1889,6168,6170],{"className":6169},[1932,2100],[1889,6171,2791],{"className":6172},[1932,2100],[1889,6174,2023],{"className":6175},[2367],[1798,6177,6178,2704],{},[1884,6179,6180],{},"关键洞见",[6182,6183,6184,6191,6407],"ol",{},[1808,6185,6186,6187,6190],{},"决策者最大化的是",[1884,6188,6189],{},"期望效用","，而非期望价值",[1808,6192,6193,6194,6239,6240,6268,6269,6352,6353,6406],{},"效用函数",[1889,6195,6197,6218],{"className":6196},[1892],[1889,6198,6200],{"className":6199},[1896],[1898,6201,6202],{"xmlns":1900},[1902,6203,6204,6215],{},[1905,6205,6206,6208,6210,6213],{},[1908,6207,5308],{},[1955,6209,1961],{"stretchy":1960},[1955,6211,6212],{},"⋅",[1955,6214,2023],{"stretchy":1960},[1912,6216,6217],{"encoding":1914},"u(\\cdot)",[1889,6219,6221],{"className":6220,"ariaHidden":1919},[1918],[1889,6222,6224,6227,6230,6233,6236],{"className":6223},[1923],[1889,6225],{"className":6226,"style":2057},[1927],[1889,6228,5308],{"className":6229},[1932,1933],[1889,6231,1961],{"className":6232},[2061],[1889,6234,6212],{"className":6235},[1932],[1889,6237,2023],{"className":6238},[2367],"在正仿射变换下唯一：如果",[1889,6241,6243,6256],{"className":6242},[1892],[1889,6244,6246],{"className":6245},[1896],[1898,6247,6248],{"xmlns":1900},[1902,6249,6250,6254],{},[1905,6251,6252],{},[1908,6253,5308],{},[1912,6255,5308],{"encoding":1914},[1889,6257,6259],{"className":6258,"ariaHidden":1919},[1918],[1889,6260,6262,6265],{"className":6261},[1923],[1889,6263],{"className":6264,"style":5332},[1927],[1889,6266,5308],{"className":6267},[1932,1933],"代表偏好，那么",[1889,6270,6272,6298],{"className":6271},[1892],[1889,6273,6275],{"className":6274},[1896],[1898,6276,6277],{"xmlns":1900},[1902,6278,6279,6295],{},[1905,6280,6281,6284,6286,6288,6290,6293],{},[1908,6282,6283],{},"v",[1955,6285,1957],{},[1908,6287,1827],{},[1955,6289,3910],{},[1908,6291,6292],{},"b",[1908,6294,5308],{},[1912,6296,6297],{"encoding":1914},"v = a + bu",[1889,6299,6301,6320,6339],{"className":6300,"ariaHidden":1919},[1918],[1889,6302,6304,6307,6311,6314,6317],{"className":6303},[1923],[1889,6305],{"className":6306,"style":5332},[1927],[1889,6308,6283],{"className":6309,"style":6310},[1932,1933],"margin-right:0.0359em;",[1889,6312],{"className":6313,"style":2043},[2042],[1889,6315,1957],{"className":6316},[2047],[1889,6318],{"className":6319,"style":2043},[2042],[1889,6321,6323,6327,6330,6333,6336],{"className":6322},[1923],[1889,6324],{"className":6325,"style":6326},[1927],"height:0.6667em;vertical-align:-0.0833em;",[1889,6328,1827],{"className":6329},[1932,1933],[1889,6331],{"className":6332,"style":4041},[2042],[1889,6334,3910],{"className":6335},[4045],[1889,6337],{"className":6338,"style":4041},[2042],[1889,6340,6342,6346,6349],{"className":6341},[1923],[1889,6343],{"className":6344,"style":6345},[1927],"height:0.6944em;",[1889,6347,6292],{"className":6348},[1932,1933],[1889,6350,5308],{"className":6351},[1932,1933],"（",[1889,6354,6356,6375],{"className":6355},[1892],[1889,6357,6359],{"className":6358},[1896],[1898,6360,6361],{"xmlns":1900},[1902,6362,6363,6372],{},[1905,6364,6365,6367,6370],{},[1908,6366,6292],{},[1955,6368,6369],{},">",[1969,6371,3819],{},[1912,6373,6374],{"encoding":1914},"b>0",[1889,6376,6378,6397],{"className":6377,"ariaHidden":1919},[1918],[1889,6379,6381,6385,6388,6391,6394],{"className":6380},[1923],[1889,6382],{"className":6383,"style":6384},[1927],"height:0.7335em;vertical-align:-0.0391em;",[1889,6386,6292],{"className":6387},[1932,1933],[1889,6389],{"className":6390,"style":2043},[2042],[1889,6392,6369],{"className":6393},[2047],[1889,6395],{"className":6396,"style":2043},[2042],[1889,6398,6400,6403],{"className":6399},[1923],[1889,6401],{"className":6402,"style":2694},[1927],[1889,6404,3819],{"className":6405},[1932],"）也代表相同偏好",[1808,6408,6409,6410,6413],{},"这是",[1884,6411,6412],{},"基数效用","（与确定性下的序数效用不同）",[1877,6415,6417],{"id":6416},"_14-圣彼得堡悖论","1.4 圣彼得堡悖论",[1798,6419,6420,6423],{},[1884,6421,6422],{},"历史背景",": 1713年，尼古拉·伯努利提出了一个著名悖论：",[1798,6425,6426,6429,6430,6458,6459,6519],{},[1884,6427,6428],{},"游戏规则",": 抛硬币直到出现正面为止。如果第",[1889,6431,6433,6446],{"className":6432},[1892],[1889,6434,6436],{"className":6435},[1896],[1898,6437,6438],{"xmlns":1900},[1902,6439,6440,6444],{},[1905,6441,6442],{},[1908,6443,2012],{},[1912,6445,2012],{"encoding":1914},[1889,6447,6449],{"className":6448,"ariaHidden":1919},[1918],[1889,6450,6452,6455],{"className":6451},[1923],[1889,6453],{"className":6454,"style":5332},[1927],[1889,6456,2012],{"className":6457},[1932,1933],"次出现正面，你赢得",[1889,6460,6462,6480],{"className":6461},[1892],[1889,6463,6465],{"className":6464},[1896],[1898,6466,6467],{"xmlns":1900},[1902,6468,6469,6477],{},[1905,6470,6471],{},[2783,6472,6473,6475],{},[1969,6474,1990],{},[1908,6476,2012],{},[1912,6478,6479],{"encoding":1914},"2^n",[1889,6481,6483],{"className":6482,"ariaHidden":1919},[1918],[1889,6484,6486,6490],{"className":6485},[1923],[1889,6487],{"className":6488,"style":6489},[1927],"height:0.6644em;",[1889,6491,6493,6496],{"className":6492},[1932],[1889,6494,1990],{"className":6495},[1932],[1889,6497,6499],{"className":6498},[2071],[1889,6500,6502],{"className":6501},[2075],[1889,6503,6505],{"className":6504},[2080],[1889,6506,6508],{"className":6507,"style":6489},[2084],[1889,6509,6510,6513],{"style":2825},[1889,6511],{"className":6512,"style":2093},[2092],[1889,6514,6516],{"className":6515},[2097,2098,2099,2100],[1889,6517,2012],{"className":6518},[1932,1933,2100],"元。你愿意付多少钱参加这个游戏？",[1798,6521,6522,2704],{},[1884,6523,6524],{},"期望价值",[1889,6526,6528],{"className":6527},[1938],[1889,6529,6531,6610],{"className":6530},[1892],[1889,6532,6534],{"className":6533},[1896],[1898,6535,6536],{"xmlns":1900,"display":1947},[1902,6537,6538,6607],{},[1905,6539,6540,6542,6544,6547,6549,6551,6566,6577,6579,6585,6587,6601,6603,6605],{},[1908,6541,5719],{"mathvariant":5313},[1955,6543,5722],{"stretchy":1960},[1908,6545,6546],{},"X",[1955,6548,5733],{"stretchy":1960},[1955,6550,1957],{},[5683,6552,6553,6555,6563],{},[1955,6554,2534],{},[1905,6556,6557,6559,6561],{},[1908,6558,2012],{},[1955,6560,1957],{},[1969,6562,1971],{},[1908,6564,6565],{"mathvariant":2789},"∞",[6567,6568,6569,6571],"mfrac",{},[1969,6570,1971],{},[2783,6572,6573,6575],{},[1969,6574,1990],{},[1908,6576,2012],{},[1955,6578,6212],{},[2783,6580,6581,6583],{},[1969,6582,1990],{},[1908,6584,2012],{},[1955,6586,1957],{},[5683,6588,6589,6591,6599],{},[1955,6590,2534],{},[1905,6592,6593,6595,6597],{},[1908,6594,2012],{},[1955,6596,1957],{},[1969,6598,1971],{},[1908,6600,6565],{"mathvariant":2789},[1969,6602,1971],{},[1955,6604,1957],{},[1908,6606,6565],{"mathvariant":2789},[1912,6608,6609],{"encoding":1914},"\\mathbb{E}[X] = \\sum_{n=1}^{\\infty} \\frac{1}{2^n} \\cdot 2^n = \\sum_{n=1}^{\\infty} 1 = \\infty",[1889,6611,6613,6641,6828,6873,6961],{"className":6612,"ariaHidden":1919},[1918],[1889,6614,6616,6619,6622,6625,6629,6632,6635,6638],{"className":6615},[1923],[1889,6617],{"className":6618,"style":2057},[1927],[1889,6620,5719],{"className":6621},[1932,5355],[1889,6623,5722],{"className":6624},[2061],[1889,6626,6546],{"className":6627,"style":6628},[1932,1933],"margin-right:0.0785em;",[1889,6630,5733],{"className":6631},[2367],[1889,6633],{"className":6634,"style":2043},[2042],[1889,6636,1957],{"className":6637},[2047],[1889,6639],{"className":6640,"style":2043},[2042],[1889,6642,6644,6648,6717,6720,6819,6822,6825],{"className":6643},[1923],[1889,6645],{"className":6646,"style":6647},[1927],"height:2.9185em;vertical-align:-1.2671em;",[1889,6649,6651],{"className":6650},[2571,5778],[1889,6652,6654,6708],{"className":6653},[2075,2076],[1889,6655,6657,6705],{"className":6656},[2080],[1889,6658,6660,6681,6691],{"className":6659,"style":5788},[2084],[1889,6661,6663,6666],{"style":6662},"top:-1.8829em;margin-left:0em;",[1889,6664],{"className":6665,"style":5795},[2092],[1889,6667,6669],{"className":6668},[2097,2098,2099,2100],[1889,6670,6672,6675,6678],{"className":6671},[1932,2100],[1889,6673,2012],{"className":6674},[1932,1933,2100],[1889,6676,1957],{"className":6677},[2047,2100],[1889,6679,1971],{"className":6680},[1932,2100],[1889,6682,6683,6686],{"style":5813},[1889,6684],{"className":6685,"style":5795},[2092],[1889,6687,6688],{},[1889,6689,2534],{"className":6690},[2571,2575,5822],[1889,6692,6693,6696],{"style":5825},[1889,6694],{"className":6695,"style":5795},[2092],[1889,6697,6699],{"className":6698},[2097,2098,2099,2100],[1889,6700,6702],{"className":6701},[1932,2100],[1889,6703,6565],{"className":6704},[1932,2100],[1889,6706,2108],{"className":6707},[2107],[1889,6709,6711],{"className":6710},[2080],[1889,6712,6715],{"className":6713,"style":6714},[2084],"height:1.2671em;",[1889,6716],{},[1889,6718],{"className":6719,"style":2125},[2042],[1889,6721,6723,6727,6816],{"className":6722},[1932],[1889,6724],{"className":6725},[2061,6726],"nulldelimiter",[1889,6728,6730],{"className":6729},[6567],[1889,6731,6733,6807],{"className":6732},[2075,2076],[1889,6734,6736,6804],{"className":6735},[2080],[1889,6737,6740,6781,6792],{"className":6738,"style":6739},[2084],"height:1.3214em;",[1889,6741,6743,6747],{"style":6742},"top:-2.314em;",[1889,6744],{"className":6745,"style":6746},[2092],"height:3em;",[1889,6748,6750],{"className":6749},[1932],[1889,6751,6753,6756],{"className":6752},[1932],[1889,6754,1990],{"className":6755},[1932],[1889,6757,6759],{"className":6758},[2071],[1889,6760,6762],{"className":6761},[2075],[1889,6763,6765],{"className":6764},[2080],[1889,6766,6769],{"className":6767,"style":6768},[2084],"height:0.5904em;",[1889,6770,6772,6775],{"style":6771},"top:-2.989em;margin-right:0.05em;",[1889,6773],{"className":6774,"style":2093},[2092],[1889,6776,6778],{"className":6777},[2097,2098,2099,2100],[1889,6779,2012],{"className":6780},[1932,1933,2100],[1889,6782,6784,6787],{"style":6783},"top:-3.23em;",[1889,6785],{"className":6786,"style":6746},[2092],[1889,6788],{"className":6789,"style":6791},[6790],"frac-line","border-bottom-width:0.04em;",[1889,6793,6795,6798],{"style":6794},"top:-3.677em;",[1889,6796],{"className":6797,"style":6746},[2092],[1889,6799,6801],{"className":6800},[1932],[1889,6802,1971],{"className":6803},[1932],[1889,6805,2108],{"className":6806},[2107],[1889,6808,6810],{"className":6809},[2080],[1889,6811,6814],{"className":6812,"style":6813},[2084],"height:0.686em;",[1889,6815],{},[1889,6817],{"className":6818},[2367,6726],[1889,6820],{"className":6821,"style":4041},[2042],[1889,6823,6212],{"className":6824},[4045],[1889,6826],{"className":6827,"style":4041},[2042],[1889,6829,6831,6835,6864,6867,6870],{"className":6830},[1923],[1889,6832],{"className":6833,"style":6834},[1927],"height:0.7144em;",[1889,6836,6838,6841],{"className":6837},[1932],[1889,6839,1990],{"className":6840},[1932],[1889,6842,6844],{"className":6843},[2071],[1889,6845,6847],{"className":6846},[2075],[1889,6848,6850],{"className":6849},[2080],[1889,6851,6853],{"className":6852,"style":6834},[2084],[1889,6854,6855,6858],{"style":3045},[1889,6856],{"className":6857,"style":2093},[2092],[1889,6859,6861],{"className":6860},[2097,2098,2099,2100],[1889,6862,2012],{"className":6863},[1932,1933,2100],[1889,6865],{"className":6866,"style":2043},[2042],[1889,6868,1957],{"className":6869},[2047],[1889,6871],{"className":6872,"style":2043},[2042],[1889,6874,6876,6879,6946,6949,6952,6955,6958],{"className":6875},[1923],[1889,6877],{"className":6878,"style":6647},[1927],[1889,6880,6882],{"className":6881},[2571,5778],[1889,6883,6885,6938],{"className":6884},[2075,2076],[1889,6886,6888,6935],{"className":6887},[2080],[1889,6889,6891,6911,6921],{"className":6890,"style":5788},[2084],[1889,6892,6893,6896],{"style":6662},[1889,6894],{"className":6895,"style":5795},[2092],[1889,6897,6899],{"className":6898},[2097,2098,2099,2100],[1889,6900,6902,6905,6908],{"className":6901},[1932,2100],[1889,6903,2012],{"className":6904},[1932,1933,2100],[1889,6906,1957],{"className":6907},[2047,2100],[1889,6909,1971],{"className":6910},[1932,2100],[1889,6912,6913,6916],{"style":5813},[1889,6914],{"className":6915,"style":5795},[2092],[1889,6917,6918],{},[1889,6919,2534],{"className":6920},[2571,2575,5822],[1889,6922,6923,6926],{"style":5825},[1889,6924],{"className":6925,"style":5795},[2092],[1889,6927,6929],{"className":6928},[2097,2098,2099,2100],[1889,6930,6932],{"className":6931},[1932,2100],[1889,6933,6565],{"className":6934},[1932,2100],[1889,6936,2108],{"className":6937},[2107],[1889,6939,6941],{"className":6940},[2080],[1889,6942,6944],{"className":6943,"style":6714},[2084],[1889,6945],{},[1889,6947],{"className":6948,"style":2125},[2042],[1889,6950,1971],{"className":6951},[1932],[1889,6953],{"className":6954,"style":2043},[2042],[1889,6956,1957],{"className":6957},[2047],[1889,6959],{"className":6960,"style":2043},[2042],[1889,6962,6964,6967],{"className":6963},[1923],[1889,6965],{"className":6966,"style":5332},[1927],[1889,6968,6565],{"className":6969},[1932],[1798,6971,6972],{},"期望价值是无穷大！但没有理性人愿意付出巨额财富参加。",[1798,6974,6975,6978,6979,6982,6983,4831],{},[1884,6976,6977],{},"解决方案 (丹尼尔·伯努利, 1738)",": 人们最大化的是期望",[1884,6980,6981],{},"效用","而非期望价值。如果",[1889,6984,6986,7020],{"className":6985},[1892],[1889,6987,6989],{"className":6988},[1896],[1898,6990,6991],{"xmlns":1900},[1902,6992,6993,7017],{},[1905,6994,6995,6997,6999,7001,7003,7005,7008,7011,7013,7015],{},[1908,6996,5308],{},[1955,6998,1961],{"stretchy":1960},[1908,7000,1967],{},[1955,7002,2023],{"stretchy":1960},[1955,7004,1957],{},[1908,7006,7007],{},"ln",[1955,7009,7010],{},"⁡",[1955,7012,1961],{"stretchy":1960},[1908,7014,1967],{},[1955,7016,2023],{"stretchy":1960},[1912,7018,7019],{"encoding":1914},"u(x) = \\ln(x)",[1889,7021,7023,7050],{"className":7022,"ariaHidden":1919},[1918],[1889,7024,7026,7029,7032,7035,7038,7041,7044,7047],{"className":7025},[1923],[1889,7027],{"className":7028,"style":2057},[1927],[1889,7030,5308],{"className":7031},[1932,1933],[1889,7033,1961],{"className":7034},[2061],[1889,7036,1967],{"className":7037},[1932,1933],[1889,7039,2023],{"className":7040},[2367],[1889,7042],{"className":7043,"style":2043},[2042],[1889,7045,1957],{"className":7046},[2047],[1889,7048],{"className":7049,"style":2043},[2042],[1889,7051,7053,7056,7059,7062,7065],{"className":7052},[1923],[1889,7054],{"className":7055,"style":2057},[1927],[1889,7057,7007],{"className":7058},[2571],[1889,7060,1961],{"className":7061},[2061],[1889,7063,1967],{"className":7064},[1932,1933],[1889,7066,2023],{"className":7067},[2367],[1889,7069,7071],{"className":7070},[1938],[1889,7072,7074,7190],{"className":7073},[1892],[1889,7075,7077],{"className":7076},[1896],[1898,7078,7079],{"xmlns":1900,"display":1947},[1902,7080,7081,7187],{},[1905,7082,7083,7085,7087,7089,7091,7093,7095,7097,7099,7113,7123,7125,7127,7129,7135,7137,7139,7153,7171,7173,7175,7177,7179,7181,7184],{},[1908,7084,5719],{"mathvariant":5313},[1955,7086,5722],{"stretchy":1960},[1908,7088,5308],{},[1955,7090,1961],{"stretchy":1960},[1908,7092,6546],{},[1955,7094,2023],{"stretchy":1960},[1955,7096,5733],{"stretchy":1960},[1955,7098,1957],{},[5683,7100,7101,7103,7111],{},[1955,7102,2534],{},[1905,7104,7105,7107,7109],{},[1908,7106,2012],{},[1955,7108,1957],{},[1969,7110,1971],{},[1908,7112,6565],{"mathvariant":2789},[6567,7114,7115,7117],{},[1969,7116,1971],{},[2783,7118,7119,7121],{},[1969,7120,1990],{},[1908,7122,2012],{},[1908,7124,7007],{},[1955,7126,7010],{},[1955,7128,1961],{"stretchy":1960},[2783,7130,7131,7133],{},[1969,7132,1990],{},[1908,7134,2012],{},[1955,7136,2023],{"stretchy":1960},[1955,7138,1957],{},[5683,7140,7141,7143,7151],{},[1955,7142,2534],{},[1905,7144,7145,7147,7149],{},[1908,7146,2012],{},[1955,7148,1957],{},[1969,7150,1971],{},[1908,7152,6565],{"mathvariant":2789},[6567,7154,7155,7165],{},[1905,7156,7157,7159,7161,7163],{},[1908,7158,2012],{},[1908,7160,7007],{},[1955,7162,7010],{},[1969,7164,1990],{},[2783,7166,7167,7169],{},[1969,7168,1990],{},[1908,7170,2012],{},[1955,7172,1957],{},[1969,7174,1990],{},[1908,7176,7007],{},[1955,7178,7010],{},[1969,7180,1990],{},[1955,7182,7183],{},"≈",[1969,7185,7186],{},"1.39",[1912,7188,7189],{"encoding":1914},"\\mathbb{E}[u(X)] = \\sum_{n=1}^{\\infty} \\frac{1}{2^n} \\ln(2^n) = \\sum_{n=1}^{\\infty} \\frac{n \\ln 2}{2^n} = 2\\ln 2 \\approx 1.39",[1889,7191,7193,7226,7440,7626,7656],{"className":7192,"ariaHidden":1919},[1918],[1889,7194,7196,7199,7202,7205,7208,7211,7214,7217,7220,7223],{"className":7195},[1923],[1889,7197],{"className":7198,"style":2057},[1927],[1889,7200,5719],{"className":7201},[1932,5355],[1889,7203,5722],{"className":7204},[2061],[1889,7206,5308],{"className":7207},[1932,1933],[1889,7209,1961],{"className":7210},[2061],[1889,7212,6546],{"className":7213,"style":6628},[1932,1933],[1889,7215,5972],{"className":7216},[2367],[1889,7218],{"className":7219,"style":2043},[2042],[1889,7221,1957],{"className":7222},[2047],[1889,7224],{"className":7225,"style":2043},[2042],[1889,7227,7229,7232,7299,7302,7390,7393,7396,7399,7428,7431,7434,7437],{"className":7228},[1923],[1889,7230],{"className":7231,"style":6647},[1927],[1889,7233,7235],{"className":7234},[2571,5778],[1889,7236,7238,7291],{"className":7237},[2075,2076],[1889,7239,7241,7288],{"className":7240},[2080],[1889,7242,7244,7264,7274],{"className":7243,"style":5788},[2084],[1889,7245,7246,7249],{"style":6662},[1889,7247],{"className":7248,"style":5795},[2092],[1889,7250,7252],{"className":7251},[2097,2098,2099,2100],[1889,7253,7255,7258,7261],{"className":7254},[1932,2100],[1889,7256,2012],{"className":7257},[1932,1933,2100],[1889,7259,1957],{"className":7260},[2047,2100],[1889,7262,1971],{"className":7263},[1932,2100],[1889,7265,7266,7269],{"style":5813},[1889,7267],{"className":7268,"style":5795},[2092],[1889,7270,7271],{},[1889,7272,2534],{"className":7273},[2571,2575,5822],[1889,7275,7276,7279],{"style":5825},[1889,7277],{"className":7278,"style":5795},[2092],[1889,7280,7282],{"className":7281},[2097,2098,2099,2100],[1889,7283,7285],{"className":7284},[1932,2100],[1889,7286,6565],{"className":7287},[1932,2100],[1889,7289,2108],{"className":7290},[2107],[1889,7292,7294],{"className":7293},[2080],[1889,7295,7297],{"className":7296,"style":6714},[2084],[1889,7298],{},[1889,7300],{"className":7301,"style":2125},[2042],[1889,7303,7305,7308,7387],{"className":7304},[1932],[1889,7306],{"className":7307},[2061,6726],[1889,7309,7311],{"className":7310},[6567],[1889,7312,7314,7379],{"className":7313},[2075,2076],[1889,7315,7317,7376],{"className":7316},[2080],[1889,7318,7320,7357,7365],{"className":7319,"style":6739},[2084],[1889,7321,7322,7325],{"style":6742},[1889,7323],{"className":7324,"style":6746},[2092],[1889,7326,7328],{"className":7327},[1932],[1889,7329,7331,7334],{"className":7330},[1932],[1889,7332,1990],{"className":7333},[1932],[1889,7335,7337],{"className":7336},[2071],[1889,7338,7340],{"className":7339},[2075],[1889,7341,7343],{"className":7342},[2080],[1889,7344,7346],{"className":7345,"style":6768},[2084],[1889,7347,7348,7351],{"style":6771},[1889,7349],{"className":7350,"style":2093},[2092],[1889,7352,7354],{"className":7353},[2097,2098,2099,2100],[1889,7355,2012],{"className":7356},[1932,1933,2100],[1889,7358,7359,7362],{"style":6783},[1889,7360],{"className":7361,"style":6746},[2092],[1889,7363],{"className":7364,"style":6791},[6790],[1889,7366,7367,7370],{"style":6794},[1889,7368],{"className":7369,"style":6746},[2092],[1889,7371,7373],{"className":7372},[1932],[1889,7374,1971],{"className":7375},[1932],[1889,7377,2108],{"className":7378},[2107],[1889,7380,7382],{"className":7381},[2080],[1889,7383,7385],{"className":7384,"style":6813},[2084],[1889,7386],{},[1889,7388],{"className":7389},[2367,6726],[1889,7391],{"className":7392,"style":2125},[2042],[1889,7394,7007],{"className":7395},[2571],[1889,7397,1961],{"className":7398},[2061],[1889,7400,7402,7405],{"className":7401},[1932],[1889,7403,1990],{"className":7404},[1932],[1889,7406,7408],{"className":7407},[2071],[1889,7409,7411],{"className":7410},[2075],[1889,7412,7414],{"className":7413},[2080],[1889,7415,7417],{"className":7416,"style":6834},[2084],[1889,7418,7419,7422],{"style":3045},[1889,7420],{"className":7421,"style":2093},[2092],[1889,7423,7425],{"className":7424},[2097,2098,2099,2100],[1889,7426,2012],{"className":7427},[1932,1933,2100],[1889,7429,2023],{"className":7430},[2367],[1889,7432],{"className":7433,"style":2043},[2042],[1889,7435,1957],{"className":7436},[2047],[1889,7438],{"className":7439,"style":2043},[2042],[1889,7441,7443,7446,7513,7516,7617,7620,7623],{"className":7442},[1923],[1889,7444],{"className":7445,"style":6647},[1927],[1889,7447,7449],{"className":7448},[2571,5778],[1889,7450,7452,7505],{"className":7451},[2075,2076],[1889,7453,7455,7502],{"className":7454},[2080],[1889,7456,7458,7478,7488],{"className":7457,"style":5788},[2084],[1889,7459,7460,7463],{"style":6662},[1889,7461],{"className":7462,"style":5795},[2092],[1889,7464,7466],{"className":7465},[2097,2098,2099,2100],[1889,7467,7469,7472,7475],{"className":7468},[1932,2100],[1889,7470,2012],{"className":7471},[1932,1933,2100],[1889,7473,1957],{"className":7474},[2047,2100],[1889,7476,1971],{"className":7477},[1932,2100],[1889,7479,7480,7483],{"style":5813},[1889,7481],{"className":7482,"style":5795},[2092],[1889,7484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风险态度与阿罗-普拉特测度",[1877,7675,7677],{"id":7676},"_21-风险态度的分类","2.1 风险态度的分类",[1798,7679,7680,7681,7710,7711,2698],{},"考虑一个公平赌博（期望价值为零）：以50%概率赢得",[1889,7682,7684,7698],{"className":7683},[1892],[1889,7685,7687],{"className":7686},[1896],[1898,7688,7689],{"xmlns":1900},[1902,7690,7691,7696],{},[1905,7692,7693],{},[1908,7694,7695],{},"h",[1912,7697,7695],{"encoding":1914},[1889,7699,7701],{"className":7700,"ariaHidden":1919},[1918],[1889,7702,7704,7707],{"className":7703},[1923],[1889,7705],{"className":7706,"style":6345},[1927],[1889,7708,7695],{"className":7709},[1932,1933],"，50%概率输",[1889,7712,7714,7727],{"className":7713},[1892],[1889,7715,7717],{"className":7716},[1896],[1898,7718,7719],{"xmlns":1900},[1902,7720,7721,7725],{},[1905,7722,7723],{},[1908,7724,7695],{},[1912,7726,7695],{"encoding":1914},[1889,7728,7730],{"className":7729,"ariaHidden":1919},[1918],[1889,7731,7733,7736],{"className":7732},[1923],[1889,7734],{"className":7735,"style":6345},[1927],[1889,7737,7695],{"className":7738},[1932,1933],[1798,7740,7741,2704],{},[1884,7742,7743],{},"定义",[1805,7745,7746,7861,7975],{},[1808,7747,7748,7751,7752],{},[1884,7749,7750],{},"风险规避 (Risk Averse)",": 偏好确定性结果而非公平赌博",[1889,7753,7755],{"className":7754},[1938],[1889,7756,7758,7800],{"className":7757},[1892],[1889,7759,7761],{"className":7760},[1896],[1898,7762,7763],{"xmlns":1900,"display":1947},[1902,7764,7765,7797],{},[1905,7766,7767,7769,7771,7773,7775,7777,7779,7781,7783,7785,7787,7789,7791,7793,7795],{},[1908,7768,5308],{},[1955,7770,1961],{"stretchy":1960},[1908,7772,5719],{"mathvariant":5313},[1955,7774,5722],{"stretchy":1960},[1908,7776,6546],{},[1955,7778,5733],{"stretchy":1960},[1955,7780,2023],{"stretchy":1960},[1955,7782,6369],{},[1908,7784,5719],{"mathvariant":5313},[1955,7786,5722],{"stretchy":1960},[1908,7788,5308],{},[1955,7790,1961],{"stretchy":1960},[1908,7792,6546],{},[1955,7794,2023],{"stretchy":1960},[1955,7796,5733],{"stretchy":1960},[1912,7798,7799],{"encoding":1914},"u(\\mathbb{E}[X]) > \\mathbb{E}[u(X)]",[1889,7801,7803,7837],{"className":7802,"ariaHidden":1919},[1918],[1889,7804,7806,7809,7812,7815,7818,7821,7824,7828,7831,7834],{"className":7805},[1923],[1889,7807],{"className":7808,"style":2057},[1927],[1889,7810,5308],{"className":7811},[1932,1933],[1889,7813,1961],{"className":7814},[2061],[1889,7816,5719],{"className":7817},[1932,5355],[1889,7819,5722],{"className":7820},[2061],[1889,7822,6546],{"className":7823,"style":6628},[1932,1933],[1889,7825,7827],{"className":7826},[2367],"])",[1889,7829],{"className":7830,"style":2043},[2042],[1889,7832,6369],{"className":7833},[2047],[1889,7835],{"className":7836,"style":2043},[2042],[1889,7838,7840,7843,7846,7849,7852,7855,7858],{"className":7839},[1923],[1889,7841],{"className":7842,"style":2057},[1927],[1889,7844,5719],{"className":7845},[1932,5355],[1889,7847,5722],{"className":7848},[2061],[1889,7850,5308],{"className":7851},[1932,1933],[1889,7853,1961],{"className":7854},[2061],[1889,7856,6546],{"className":7857,"style":6628},[1932,1933],[1889,7859,5972],{"className":7860},[2367],[1808,7862,7863,7866,7867],{},[1884,7864,7865],{},"风险中性 (Risk Neutral)",": 对赌博和确定性等价无差异",[1889,7868,7870],{"className":7869},[1938],[1889,7871,7873,7915],{"className":7872},[1892],[1889,7874,7876],{"className":7875},[1896],[1898,7877,7878],{"xmlns":1900,"display":1947},[1902,7879,7880,7912],{},[1905,7881,7882,7884,7886,7888,7890,7892,7894,7896,7898,7900,7902,7904,7906,7908,7910],{},[1908,7883,5308],{},[1955,7885,1961],{"stretchy":1960},[1908,7887,5719],{"mathvariant":5313},[1955,7889,5722],{"stretchy":1960},[1908,7891,6546],{},[1955,7893,5733],{"stretchy":1960},[1955,7895,2023],{"stretchy":1960},[1955,7897,1957],{},[1908,7899,5719],{"mathvariant":5313},[1955,7901,5722],{"stretchy":1960},[1908,7903,5308],{},[1955,7905,1961],{"stretchy":1960},[1908,7907,6546],{},[1955,7909,2023],{"stretchy":1960},[1955,7911,5733],{"stretchy":1960},[1912,7913,7914],{"encoding":1914},"u(\\mathbb{E}[X]) = \\mathbb{E}[u(X)]",[1889,7916,7918,7951],{"className":7917,"ariaHidden":1919},[1918],[1889,7919,7921,7924,7927,7930,7933,7936,7939,7942,7945,7948],{"className":7920},[1923],[1889,7922],{"className":7923,"style":2057},[1927],[1889,7925,5308],{"className":7926},[1932,1933],[1889,7928,1961],{"className":7929},[2061],[1889,7931,5719],{"className":7932},[1932,5355],[1889,7934,5722],{"className":7935},[2061],[1889,7937,6546],{"className":7938,"style":6628},[1932,1933],[1889,7940,7827],{"className":7941},[2367],[1889,7943],{"className":7944,"style":2043},[2042],[1889,7946,1957],{"className":7947},[2047],[1889,7949],{"className":7950,"style":2043},[2042],[1889,7952,7954,7957,7960,7963,7966,7969,7972],{"className":7953},[1923],[1889,7955],{"className":7956,"style":2057},[1927],[1889,7958,5719],{"className":7959},[1932,5355],[1889,7961,5722],{"className":7962},[2061],[1889,7964,5308],{"className":7965},[1932,1933],[1889,7967,1961],{"className":7968},[2061],[1889,7970,6546],{"className":7971,"style":6628},[1932,1933],[1889,7973,5972],{"className":7974},[2367],[1808,7976,7977,7980,7981],{},[1884,7978,7979],{},"风险爱好 (Risk Loving)",": 偏好赌博而非确定性结果",[1889,7982,7984],{"className":7983},[1938],[1889,7985,7987,8030],{"className":7986},[1892],[1889,7988,7990],{"className":7989},[1896],[1898,7991,7992],{"xmlns":1900,"display":1947},[1902,7993,7994,8027],{},[1905,7995,7996,7998,8000,8002,8004,8006,8008,8010,8013,8015,8017,8019,8021,8023,8025],{},[1908,7997,5308],{},[1955,7999,1961],{"stretchy":1960},[1908,8001,5719],{"mathvariant":5313},[1955,8003,5722],{"stretchy":1960},[1908,8005,6546],{},[1955,8007,5733],{"stretchy":1960},[1955,8009,2023],{"stretchy":1960},[1955,8011,8012],{},"\u003C",[1908,8014,5719],{"mathvariant":5313},[1955,8016,5722],{"stretchy":1960},[1908,8018,5308],{},[1955,8020,1961],{"stretchy":1960},[1908,8022,6546],{},[1955,8024,2023],{"stretchy":1960},[1955,8026,5733],{"stretchy":1960},[1912,8028,8029],{"encoding":1914},"u(\\mathbb{E}[X]) \u003C \\mathbb{E}[u(X)]",[1889,8031,8033,8066],{"className":8032,"ariaHidden":1919},[1918],[1889,8034,8036,8039,8042,8045,8048,8051,8054,8057,8060,8063],{"className":8035},[1923],[1889,8037],{"className":8038,"style":2057},[1927],[1889,8040,5308],{"className":8041},[1932,1933],[1889,8043,1961],{"className":8044},[2061],[1889,8046,5719],{"className":8047},[1932,5355],[1889,8049,5722],{"className":8050},[2061],[1889,8052,6546],{"className":8053,"style":6628},[1932,1933],[1889,8055,7827],{"className":8056},[2367],[1889,8058],{"className":8059,"style":2043},[2042],[1889,8061,8012],{"className":8062},[2047],[1889,8064],{"className":8065,"style":2043},[2042],[1889,8067,8069,8072,8075,8078,8081,8084,8087],{"className":8068},[1923],[1889,8070],{"className":8071,"style":2057},[1927],[1889,8073,5719],{"className":8074},[1932,5355],[1889,8076,5722],{"className":8077},[2061],[1889,8079,5308],{"className":8080},[1932,1933],[1889,8082,1961],{"className":8083},[2061],[1889,8085,6546],{"className":8086,"style":6628},[1932,1933],[1889,8088,5972],{"className":8089},[2367],[1798,8091,8092,2704],{},[1884,8093,8094],{},"与效用函数形状的关系",[1805,8096,8097,8209,8318],{},[1808,8098,8099,8100,8204,8205,8208],{},"风险规避 ⟺ ",[1889,8101,8103,8135],{"className":8102},[1892],[1889,8104,8106],{"className":8105},[1896],[1898,8107,8108],{"xmlns":1900},[1902,8109,8110,8132],{},[1905,8111,8112,8122,8124,8126,8128,8130],{},[2783,8113,8114,8116],{},[1908,8115,5308],{},[1905,8117,8118,8120],{},[1955,8119,2791],{"mathvariant":2789},[1955,8121,2791],{"mathvariant":2789},[1955,8123,1961],{"stretchy":1960},[1908,8125,1967],{},[1955,8127,2023],{"stretchy":1960},[1955,8129,8012],{},[1969,8131,3819],{},[1912,8133,8134],{"encoding":1914},"u''(x) \u003C 0",[1889,8136,8138,8195],{"className":8137,"ariaHidden":1919},[1918],[1889,8139,8141,8144,8177,8180,8183,8186,8189,8192],{"className":8140},[1923],[1889,8142],{"className":8143,"style":6134},[1927],[1889,8145,8147,8150],{"className":8146},[1932],[1889,8148,5308],{"className":8149},[1932,1933],[1889,8151,8153],{"className":8152},[2071],[1889,8154,8156],{"className":8155},[2075],[1889,8157,8159],{"className":8158},[2080],[1889,8160,8162],{"className":8161,"style":2804},[2084],[1889,8163,8164,8167],{"style":2825},[1889,8165],{"className":8166,"style":2093},[2092],[1889,8168,8170],{"className":8169},[2097,2098,2099,2100],[1889,8171,8173],{"className":8172},[1932,2100],[1889,8174,8176],{"className":8175},[1932,2100],"′′",[1889,8178,1961],{"className":8179},[2061],[1889,8181,1967],{"className":8182},[1932,1933],[1889,8184,2023],{"className":8185},[2367],[1889,8187],{"className":8188,"style":2043},[2042],[1889,8190,8012],{"className":8191},[2047],[1889,8193],{"className":8194,"style":2043},[2042],[1889,8196,8198,8201],{"className":8197},[1923],[1889,8199],{"className":8200,"style":2694},[1927],[1889,8202,3819],{"className":8203},[1932]," ⟺ 效用函数",[1884,8206,8207],{},"凹","（边际效用递减）",[1808,8210,8211,8212,8204,8315],{},"风险中性 ⟺ ",[1889,8213,8215,8247],{"className":8214},[1892],[1889,8216,8218],{"className":8217},[1896],[1898,8219,8220],{"xmlns":1900},[1902,8221,8222,8244],{},[1905,8223,8224,8234,8236,8238,8240,8242],{},[2783,8225,8226,8228],{},[1908,8227,5308],{},[1905,8229,8230,8232],{},[1955,8231,2791],{"mathvariant":2789},[1955,8233,2791],{"mathvariant":2789},[1955,8235,1961],{"stretchy":1960},[1908,8237,1967],{},[1955,8239,2023],{"stretchy":1960},[1955,8241,1957],{},[1969,8243,3819],{},[1912,8245,8246],{"encoding":1914},"u''(x) = 0",[1889,8248,8250,8306],{"className":8249,"ariaHidden":1919},[1918],[1889,8251,8253,8256,8288,8291,8294,8297,8300,8303],{"className":8252},[1923],[1889,8254],{"className":8255,"style":6134},[1927],[1889,8257,8259,8262],{"className":8258},[1932],[1889,8260,5308],{"className":8261},[1932,1933],[1889,8263,8265],{"className":8264},[2071],[1889,8266,8268],{"className":8267},[2075],[1889,8269,8271],{"className":8270},[2080],[1889,8272,8274],{"className":8273,"style":2804},[2084],[1889,8275,8276,8279],{"style":2825},[1889,8277],{"className":8278,"style":2093},[2092],[1889,8280,8282],{"className":8281},[2097,2098,2099,2100],[1889,8283,8285],{"className":8284},[1932,2100],[1889,8286,8176],{"className":8287},[1932,2100],[1889,8289,1961],{"className":8290},[2061],[1889,8292,1967],{"className":8293},[1932,1933],[1889,8295,2023],{"className":8296},[2367],[1889,8298],{"className":8299,"style":2043},[2042],[1889,8301,1957],{"className":8302},[2047],[1889,8304],{"className":8305,"style":2043},[2042],[1889,8307,8309,8312],{"className":8308},[1923],[1889,8310],{"className":8311,"style":2694},[1927],[1889,8313,3819],{"className":8314},[1932],[1884,8316,8317],{},"线性",[1808,8319,8320,8321,8204,8424],{},"风险爱好 ⟺ ",[1889,8322,8324,8356],{"className":8323},[1892],[1889,8325,8327],{"className":8326},[1896],[1898,8328,8329],{"xmlns":1900},[1902,8330,8331,8353],{},[1905,8332,8333,8343,8345,8347,8349,8351],{},[2783,8334,8335,8337],{},[1908,8336,5308],{},[1905,8338,8339,8341],{},[1955,8340,2791],{"mathvariant":2789},[1955,8342,2791],{"mathvariant":2789},[1955,8344,1961],{"stretchy":1960},[1908,8346,1967],{},[1955,8348,2023],{"stretchy":1960},[1955,8350,6369],{},[1969,8352,3819],{},[1912,8354,8355],{"encoding":1914},"u''(x) > 0",[1889,8357,8359,8415],{"className":8358,"ariaHidden":1919},[1918],[1889,8360,8362,8365,8397,8400,8403,8406,8409,8412],{"className":8361},[1923],[1889,8363],{"className":8364,"style":6134},[1927],[1889,8366,8368,8371],{"className":8367},[1932],[1889,8369,5308],{"className":8370},[1932,1933],[1889,8372,8374],{"className":8373},[2071],[1889,8375,8377],{"className":8376},[2075],[1889,8378,8380],{"className":8379},[2080],[1889,8381,8383],{"className":8382,"style":2804},[2084],[1889,8384,8385,8388],{"style":2825},[1889,8386],{"className":8387,"style":2093},[2092],[1889,8389,8391],{"className":8390},[2097,2098,2099,2100],[1889,8392,8394],{"className":8393},[1932,2100],[1889,8395,8176],{"className":8396},[1932,2100],[1889,8398,1961],{"className":8399},[2061],[1889,8401,1967],{"className":8402},[1932,1933],[1889,8404,2023],{"className":8405},[2367],[1889,8407],{"className":8408,"style":2043},[2042],[1889,8410,6369],{"className":8411},[2047],[1889,8413],{"className":8414,"style":2043},[2042],[1889,8416,8418,8421],{"className":8417},[1923],[1889,8419],{"className":8420,"style":2694},[1927],[1889,8422,3819],{"className":8423},[1932],[1884,8425,8426],{},"凸",[1798,8428,8429,8432],{},[1884,8430,8431],{},"证明"," (风险规避情况):\n对于小赌注，泰勒展开：",[1889,8434,8436],{"className":8435},[1938],[1889,8437,8439,8632],{"className":8438},[1892],[1889,8440,8442],{"className":8441},[1896],[1898,8443,8444],{"xmlns":1900,"display":1947},[1902,8445,8446,8629],{},[8447,8448,8451,8572],"mtable",{"rowspacing":8449,"columnalign":8450,"columnspacing":2790},"0.25em","right left",[8452,8453,8454,8488],"mtr",{},[8455,8456,8457],"mtd",{},[8458,8459,8460],"mstyle",{"scriptlevel":3819,"displaystyle":1919},[1905,8461,8462,8464,8466,8468,8470,8473,8475,8484,8486],{},[1908,8463,5719],{"mathvariant":5313},[1955,8465,5722],{"stretchy":1960},[1908,8467,5308],{},[1955,8469,1961],{"stretchy":1960},[1908,8471,8472],{},"w",[1955,8474,3910],{},[8476,8477,8478,8481],"mover",{"accent":1919},[1908,8479,8480],{},"ϵ",[1955,8482,8483],{},"~",[1955,8485,2023],{"stretchy":1960},[1955,8487,5733],{"stretchy":1960},[8455,8489,8490],{},[8458,8491,8492],{"scriptlevel":3819,"displaystyle":1919},[1905,8493,8494,8496,8498,8500,8502,8504,8506,8508,8514,8516,8518,8520,8522,8524,8530,8532,8534,8540,8550,8552,8554,8556,8558,8560,8570],{},[1905,8495],{},[1955,8497,7183],{},[1908,8499,5308],{},[1955,8501,1961],{"stretchy":1960},[1908,8503,8472],{},[1955,8505,2023],{"stretchy":1960},[1955,8507,3910],{},[2783,8509,8510,8512],{},[1908,8511,5308],{},[1955,8513,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,8515,1961],{"stretchy":1960},[1908,8517,8472],{},[1955,8519,2023],{"stretchy":1960},[1908,8521,5719],{"mathvariant":5313},[1955,8523,5722],{"stretchy":1960},[8476,8525,8526,8528],{"accent":1919},[1908,8527,8480],{},[1955,8529,8483],{},[1955,8531,5733],{"stretchy":1960},[1955,8533,3910],{},[6567,8535,8536,8538],{},[1969,8537,1971],{},[1969,8539,1990],{},[2783,8541,8542,8544],{},[1908,8543,5308],{},[1905,8545,8546,8548],{},[1955,8547,2791],{"mathvariant":2789},[1955,8549,2791],{"mathvariant":2789},[1955,8551,1961],{"stretchy":1960},[1908,8553,8472],{},[1955,8555,2023],{"stretchy":1960},[1908,8557,5719],{"mathvariant":5313},[1955,8559,5722],{"stretchy":1960},[2783,8561,8562,8568],{},[8476,8563,8564,8566],{"accent":1919},[1908,8565,8480],{},[1955,8567,8483],{},[1969,8569,1990],{},[1955,8571,5733],{"stretchy":1960},[8452,8573,8574,8580],{},[8455,8575,8576],{},[8458,8577,8578],{"scriptlevel":3819,"displaystyle":1919},[1905,8579],{},[8455,8581,8582],{},[8458,8583,8584],{"scriptlevel":3819,"displaystyle":1919},[1905,8585,8586,8588,8590,8592,8594,8596,8598,8600,8606,8616,8618,8620,8622],{},[1905,8587],{},[1955,8589,1957],{},[1908,8591,5308],{},[1955,8593,1961],{"stretchy":1960},[1908,8595,8472],{},[1955,8597,2023],{"stretchy":1960},[1955,8599,3910],{},[6567,8601,8602,8604],{},[1969,8603,1971],{},[1969,8605,1990],{},[2783,8607,8608,8610],{},[1908,8609,5308],{},[1905,8611,8612,8614],{},[1955,8613,2791],{"mathvariant":2789},[1955,8615,2791],{"mathvariant":2789},[1955,8617,1961],{"stretchy":1960},[1908,8619,8472],{},[1955,8621,2023],{"stretchy":1960},[2783,8623,8624,8627],{},[1908,8625,8626],{},"σ",[1969,8628,1990],{},[1912,8630,8631],{"encoding":1914},"\\begin{align*}\n\\mathbb{E}[u(w + \\tilde{\\epsilon})] &\\approx u(w) + u'(w)\\mathbb{E}[\\tilde{\\epsilon}] + \\frac{1}{2}u''(w)\\mathbb{E}[\\tilde{\\epsilon}^2] \\\\\n&= u(w) + \\frac{1}{2}u''(w)\\sigma^2\n\\end{align*}",[1889,8633,8635],{"className":8634,"ariaHidden":1919},[1918],[1889,8636,8638,8642],{"className":8637},[1923],[1889,8639],{"className":8640,"style":8641},[1927],"height:4.3149em;vertical-align:-1.9074em;",[1889,8643,8645],{"className":8644},[1932],[1889,8646,8648,8758],{"className":8647},[8447],[1889,8649,8652],{"className":8650},[8651],"col-align-r",[1889,8653,8655,8749],{"className":8654},[2075,2076],[1889,8656,8658,8746],{"className":8657},[2080],[1889,8659,8662,8737],{"className":8660,"style":8661},[2084],"height:2.4074em;",[1889,8663,8665,8669],{"style":8664},"top:-4.4074em;",[1889,8666],{"className":8667,"style":8668},[2092],"height:3.3214em;",[1889,8670,8672,8675,8678,8681,8684,8688,8691,8694,8697,8734],{"className":8671},[1932],[1889,8673,5719],{"className":8674},[1932,5355],[1889,8676,5722],{"className":8677},[2061],[1889,8679,5308],{"className":8680},[1932,1933],[1889,8682,1961],{"className":8683},[2061],[1889,8685,8472],{"className":8686,"style":8687},[1932,1933],"margin-right:0.0269em;",[1889,8689],{"className":8690,"style":4041},[2042],[1889,8692,3910],{"className":8693},[4045],[1889,8695],{"className":8696,"style":4041},[2042],[1889,8698,8701],{"className":8699},[1932,8700],"accent",[1889,8702,8704],{"className":8703},[2075],[1889,8705,8707],{"className":8706},[2080],[1889,8708,8711,8720],{"className":8709,"style":8710},[2084],"height:0.6679em;",[1889,8712,8714,8717],{"style":8713},"top:-3em;",[1889,8715],{"className":8716,"style":6746},[2092],[1889,8718,8480],{"className":8719},[1932,1933],[1889,8721,8723,8726],{"style":8722},"top:-3.35em;",[1889,8724],{"className":8725,"style":6746},[2092],[1889,8727,8731],{"className":8728,"style":8730},[8729],"accent-body","left:-0.1944em;",[1889,8732,8483],{"className":8733},[1932],[1889,8735,5972],{"className":8736},[2367],[1889,8738,8740,8743],{"style":8739},"top:-2.1em;",[1889,8741],{"className":8742,"style":8668},[2092],[1889,8744],{"className":8745},[1932],[1889,8747,2108],{"className":8748},[2107],[1889,8750,8752],{"className":8751},[2080],[1889,8753,8756],{"className":8754,"style":8755},[2084],"height:1.9074em;",[1889,8757],{},[1889,8759,8762],{"className":8760},[8761],"col-align-l",[1889,8763,8765,9248],{"className":8764},[2075,2076],[1889,8766,8768,9245],{"className":8767},[2080],[1889,8769,8771,9072],{"className":8770,"style":8661},[2084],[1889,8772,8773,8776],{"style":8664},[1889,8774],{"className":8775,"style":8668},[2092],[1889,8777,8779,8782,8785,8788,8791,8794,8797,8800,8803,8806,8809,8812,8844,8847,8850,8853,8856,8859,8890,8893,8896,8899,8902,8964,8996,8999,9002,9005,9008,9011,9069],{"className":8778},[1932],[1889,8780],{"className":8781},[1932],[1889,8783],{"className":8784,"style":2043},[2042],[1889,8786,7183],{"className":8787},[2047],[1889,8789],{"className":8790,"style":2043},[2042],[1889,8792,5308],{"className":8793},[1932,1933],[1889,8795,1961],{"className":8796},[2061],[1889,8798,8472],{"className":8799,"style":8687},[1932,1933],[1889,8801,2023],{"className":8802},[2367],[1889,8804],{"className":8805,"style":4041},[2042],[1889,8807,3910],{"className":8808},[4045],[1889,8810],{"className":8811,"style":4041},[2042],[1889,8813,8815,8818],{"className":8814},[1932],[1889,8816,5308],{"className":8817},[1932,1933],[1889,8819,8821],{"className":8820},[2071],[1889,8822,8824],{"className":8823},[2075],[1889,8825,8827],{"className":8826},[2080],[1889,8828,8830],{"className":8829,"style":3042},[2084],[1889,8831,8832,8835],{"style":3045},[1889,8833],{"className":8834,"style":2093},[2092],[1889,8836,8838],{"className":8837},[2097,2098,2099,2100],[1889,8839,8841],{"className":8840},[1932,2100],[1889,8842,2791],{"className":8843},[1932,2100],[1889,8845,1961],{"className":8846},[2061],[1889,8848,8472],{"className":8849,"style":8687},[1932,1933],[1889,8851,2023],{"className":8852},[2367],[1889,8854,5719],{"className":8855},[1932,5355],[1889,8857,5722],{"className":8858},[2061],[1889,8860,8862],{"className":8861},[1932,8700],[1889,8863,8865],{"className":8864},[2075],[1889,8866,8868],{"className":8867},[2080],[1889,8869,8871,8879],{"className":8870,"style":8710},[2084],[1889,8872,8873,8876],{"style":8713},[1889,8874],{"className":8875,"style":6746},[2092],[1889,8877,8480],{"className":8878},[1932,1933],[1889,8880,8881,8884],{"style":8722},[1889,8882],{"className":8883,"style":6746},[2092],[1889,8885,8887],{"className":8886,"style":8730},[8729],[1889,8888,8483],{"className":8889},[1932],[1889,8891,5733],{"className":8892},[2367],[1889,8894],{"className":8895,"style":4041},[2042],[1889,8897,3910],{"className":8898},[4045],[1889,8900],{"className":8901,"style":4041},[2042],[1889,8903,8905,8908,8961],{"className":8904},[1932],[1889,8906],{"className":8907},[2061,6726],[1889,8909,8911],{"className":8910},[6567],[1889,8912,8914,8953],{"className":8913},[2075,2076],[1889,8915,8917,8950],{"className":8916},[2080],[1889,8918,8920,8931,8939],{"className":8919,"style":6739},[2084],[1889,8921,8922,8925],{"style":6742},[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确定性等价与风险溢价",[1798,9515,9516,9519],{},[1884,9517,9518],{},"确定性等价 (Certainty Equivalent, CE)",": 使得决策者在确定获得CE和接受赌博之间无差异的确定金额。",[1889,9521,9523],{"className":9522},[1938],[1889,9524,9526,9569],{"className":9525},[1892],[1889,9527,9529],{"className":9528},[1896],[1898,9530,9531],{"xmlns":1900,"display":1947},[1902,9532,9533,9566],{},[1905,9534,9535,9537,9539,9542,9544,9546,9548,9550,9552,9554,9556,9562,9564],{},[1908,9536,5308],{},[1955,9538,1961],{"stretchy":1960},[1908,9540,9541],{},"C",[1908,9543,5719],{},[1955,9545,2023],{"stretchy":1960},[1955,9547,1957],{},[1908,9549,5719],{"mathvariant":5313},[1955,9551,5722],{"stretchy":1960},[1908,9553,5308],{},[1955,9555,1961],{"stretchy":1960},[8476,9557,9558,9560],{"accent":1919},[1908,9559,8472],{},[1955,9561,8483],{},[1955,9563,2023],{"stretchy":1960},[1955,9565,5733],{"stretchy":1960},[1912,9567,9568],{"encoding":1914},"u(CE) = \\mathbb{E}[u(\\tilde{w})]",[1889,9570,9572,9604],{"className":9571,"ariaHidden":1919},[1918],[1889,9573,9575,9578,9581,9584,9588,9592,9595,9598,9601],{"className":9574},[1923],[1889,9576],{"className":9577,"style":2057},[1927],[1889,9579,5308],{"className":9580},[1932,1933],[1889,9582,1961],{"className":9583},[2061],[1889,9585,9541],{"className":9586,"style":9587},[1932,1933],"margin-right:0.0715em;",[1889,9589,5719],{"className":9590,"style":9591},[1932,1933],"margin-right:0.0576em;",[1889,9593,2023],{"className":9594},[2367],[1889,9596],{"className":9597,"style":2043},[2042],[1889,9599,1957],{"className":9600},[2047],[1889,9602],{"className":9603,"style":2043},[2042],[1889,9605,9607,9610,9613,9616,9619,9622,9654],{"className":9606},[1923],[1889,9608],{"className":9609,"style":2057},[1927],[1889,9611,5719],{"className":9612},[1932,5355],[1889,9614,5722],{"className":9615},[2061],[1889,9617,5308],{"className":9618},[1932,1933],[1889,9620,1961],{"className":9621},[2061],[1889,9623,9625],{"className":9624},[1932,8700],[1889,9626,9628],{"className":9627},[2075],[1889,9629,9631],{"className":9630},[2080],[1889,9632,9634,9642],{"className":9633,"style":8710},[2084],[1889,9635,9636,9639],{"style":8713},[1889,9637],{"className":9638,"style":6746},[2092],[1889,9640,8472],{"className":9641,"style":8687},[1932,1933],[1889,9643,9644,9647],{"style":8722},[1889,9645],{"className":9646,"style":6746},[2092],[1889,9648,9651],{"className":9649,"style":9650},[8729],"left:-0.1667em;",[1889,9652,8483],{"className":9653},[1932],[1889,9655,5972],{"className":9656},[2367],[1798,9658,9659,9662],{},[1884,9660,9661],{},"风险溢价 (Risk Premium, RP)",": 决策者为了避免风险愿意放弃的金额。",[1889,9664,9666],{"className":9665},[1938],[1889,9667,9669,9706],{"className":9668},[1892],[1889,9670,9672],{"className":9671},[1896],[1898,9673,9674],{"xmlns":1900,"display":1947},[1902,9675,9676,9703],{},[1905,9677,9678,9680,9683,9685,9687,9689,9695,9697,9699,9701],{},[1908,9679,5314],{},[1908,9681,9682],{},"P",[1955,9684,1957],{},[1908,9686,5719],{"mathvariant":5313},[1955,9688,5722],{"stretchy":1960},[8476,9690,9691,9693],{"accent":1919},[1908,9692,8472],{},[1955,9694,8483],{},[1955,9696,5733],{"stretchy":1960},[1955,9698,3917],{},[1908,9700,9541],{},[1908,9702,5719],{},[1912,9704,9705],{"encoding":1914},"RP = \\mathbb{E}[\\tilde{w}] - CE",[1889,9707,9709,9732,9787],{"className":9708,"ariaHidden":1919},[1918],[1889,9710,9712,9715,9719,9723,9726,9729],{"className":9711},[1923],[1889,9713],{"className":9714,"style":1928},[1927],[1889,9716,5314],{"className":9717,"style":9718},[1932,1933],"margin-right:0.0077em;",[1889,9720,9682],{"className":9721,"style":9722},[1932,1933],"margin-right:0.1389em;",[1889,9724],{"className":9725,"style":2043},[2042],[1889,9727,1957],{"className":9728},[2047],[1889,9730],{"className":9731,"style":2043},[2042],[1889,9733,9735,9738,9741,9744,9775,9778,9781,9784],{"className":9734},[1923],[1889,9736],{"className":9737,"style":2057},[1927],[1889,9739,5719],{"className":9740},[1932,5355],[1889,9742,5722],{"className":9743},[2061],[1889,9745,9747],{"className":9746},[1932,8700],[1889,9748,9750],{"className":9749},[2075],[1889,9751,9753],{"className":9752},[2080],[1889,9754,9756,9764],{"className":9755,"style":8710},[2084],[1889,9757,9758,9761],{"style":8713},[1889,9759],{"className":9760,"style":6746},[2092],[1889,9762,8472],{"className":9763,"style":8687},[1932,1933],[1889,9765,9766,9769],{"style":8722},[1889,9767],{"className":9768,"style":6746},[2092],[1889,9770,9772],{"className":9771,"style":9650},[8729],[1889,9773,8483],{"className":9774},[1932],[1889,9776,5733],{"className":9777},[2367],[1889,9779],{"className":9780,"style":4041},[2042],[1889,9782,3917],{"className":9783},[4045],[1889,9785],{"className":9786,"style":4041},[2042],[1889,9788,9790,9793,9796],{"className":9789},[1923],[1889,9791],{"className":9792,"style":1928},[1927],[1889,9794,9541],{"className":9795,"style":9587},[1932,1933],[1889,9797,5719],{"className":9798,"style":9591},[1932,1933],[1798,9800,9801,2704],{},[1884,9802,9803],{},"几何解释",[9805,9806,9810],"pre",{"className":9807,"code":9809,"language":3065},[9808],"language-text","u(w)\n  ↑      \n  │     ╱\n  │   ╱  ╲\n  │ ╱      ╲  ← 效用函数 u(w)\n  ├────────●  ← 期望效用 E[u(w̃)]\n  │        │\n  │        │\n  ├────────┼────●\n  │   CE   │ E[w̃]\n  │←──RP──→│\n  └────────┴────→ w\n",[9811,9812,9809],"code",{"__ignoreMap":10},[1877,9814,9816],{"id":9815},"_23-阿罗-普拉特测度","2.3 阿罗-普拉特测度",[1798,9818,9819,2704],{},[1884,9820,9821],{},"绝对风险规避系数 (Absolute Risk Aversion, ARA)",[1889,9823,9825],{"className":9824},[1938],[1889,9826,9828,9887],{"className":9827},[1892],[1889,9829,9831],{"className":9830},[1896],[1898,9832,9833],{"xmlns":1900,"display":1947},[1902,9834,9835,9884],{},[1905,9836,9837,9840,9842,9844,9846,9848,9850],{},[1908,9838,9839],{},"A",[1955,9841,1961],{"stretchy":1960},[1908,9843,8472],{},[1955,9845,2023],{"stretchy":1960},[1955,9847,1957],{},[1955,9849,3917],{},[6567,9851,9852,9870],{},[1905,9853,9854,9864,9866,9868],{},[2783,9855,9856,9858],{},[1908,9857,5308],{},[1905,9859,9860,9862],{},[1955,9861,2791],{"mathvariant":2789},[1955,9863,2791],{"mathvariant":2789},[1955,9865,1961],{"stretchy":1960},[1908,9867,8472],{},[1955,9869,2023],{"stretchy":1960},[1905,9871,9872,9878,9880,9882],{},[2783,9873,9874,9876],{},[1908,9875,5308],{},[1955,9877,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,9879,1961],{"stretchy":1960},[1908,9881,8472],{},[1955,9883,2023],{"stretchy":1960},[1912,9885,9886],{"encoding":1914},"A(w) = -\\frac{u''(w)}{u'(w)}",[1889,9888,9890,9917],{"className":9889,"ariaHidden":1919},[1918],[1889,9891,9893,9896,9899,9902,9905,9908,9911,9914],{"className":9892},[1923],[1889,9894],{"className":9895,"style":2057},[1927],[1889,9897,9839],{"className":9898},[1932,1933],[1889,9900,1961],{"className":9901},[2061],[1889,9903,8472],{"className":9904,"style":8687},[1932,1933],[1889,9906,2023],{"className":9907},[2367],[1889,9909],{"className":9910,"style":2043},[2042],[1889,9912,1957],{"className":9913},[2047],[1889,9915],{"className":9916,"style":2043},[2042],[1889,9918,9920,9924,9927],{"className":9919},[1923],[1889,9921],{"className":9922,"style":9923},[1927],"height:2.3649em;vertical-align:-0.936em;",[1889,9925,3917],{"className":9926},[1932],[1889,9928,9930,9933,10065],{"className":9929},[1932],[1889,9931],{"className":9932},[2061,6726],[1889,9934,9936],{"className":9935},[6567],[1889,9937,9939,10056],{"className":9938},[2075,2076],[1889,9940,9942,10053],{"className":9941},[2080],[1889,9943,9946,9996,10004],{"className":9944,"style":9945},[2084],"height:1.4289em;",[1889,9947,9948,9951],{"style":6742},[1889,9949],{"className":9950,"style":6746},[2092],[1889,9952,9954,9987,9990,9993],{"className":9953},[1932],[1889,9955,9957,9960],{"className":9956},[1932],[1889,9958,5308],{"className":9959},[1932,1933],[1889,9961,9963],{"className":9962},[2071],[1889,9964,9966],{"className":9965},[2075],[1889,9967,9969],{"className":9968},[2080],[1889,9970,9973],{"className":9971,"style":9972},[2084],"height:0.6779em;",[1889,9974,9975,9978],{"style":6771},[1889,9976],{"className":9977,"style":2093},[2092],[1889,9979,9981],{"className":9980},[2097,2098,2099,2100],[1889,9982,9984],{"className":9983},[1932,2100],[1889,9985,2791],{"className":9986},[1932,2100],[1889,9988,1961],{"className":9989},[2061],[1889,9991,8472],{"className":9992,"style":8687},[1932,1933],[1889,9994,2023],{"className":9995},[2367],[1889,9997,9998,10001],{"style":6783},[1889,9999],{"className":10000,"style":6746},[2092],[1889,10002],{"className":10003,"style":6791},[6790],[1889,10005,10006,10009],{"style":6794},[1889,10007],{"className":10008,"style":6746},[2092],[1889,10010,10012,10044,10047,10050],{"className":10011},[1932],[1889,10013,10015,10018],{"className":10014},[1932],[1889,10016,5308],{"className":10017},[1932,1933],[1889,10019,10021],{"className":10020},[2071],[1889,10022,10024],{"className":10023},[2075],[1889,10025,10027],{"className":10026},[2080],[1889,10028,10030],{"className":10029,"style":2804},[2084],[1889,10031,10032,10035],{"style":2825},[1889,10033],{"className":10034,"style":2093},[2092],[1889,10036,10038],{"className":10037},[2097,2098,2099,2100],[1889,10039,10041],{"className":10040},[1932,2100],[1889,10042,8176],{"className":10043},[1932,2100],[1889,10045,1961],{"className":10046},[2061],[1889,10048,8472],{"className":10049,"style":8687},[1932,1933],[1889,10051,2023],{"className":10052},[2367],[1889,10054,2108],{"className":10055},[2107],[1889,10057,10059],{"className":10058},[2080],[1889,10060,10063],{"className":10061,"style":10062},[2084],"height:0.936em;",[1889,10064],{},[1889,10066],{"className":10067},[2367,6726],[1798,10069,10070,2704],{},[1884,10071,10072],{},"相对风险规避系数 (Relative Risk Aversion, RRA)",[1889,10074,10076],{"className":10075},[1938],[1889,10077,10079,10155],{"className":10078},[1892],[1889,10080,10082],{"className":10081},[1896],[1898,10083,10084],{"xmlns":1900,"display":1947},[1902,10085,10086,10152],{},[1905,10087,10088,10090,10092,10094,10096,10098,10100,10138,10140,10142,10144,10146,10148,10150],{},[1908,10089,5314],{},[1955,10091,1961],{"stretchy":1960},[1908,10093,8472],{},[1955,10095,2023],{"stretchy":1960},[1955,10097,1957],{},[1955,10099,3917],{},[6567,10101,10102,10124],{},[1905,10103,10104,10106,10108,10118,10120,10122],{},[1908,10105,8472],{},[1955,10107,6212],{},[2783,10109,10110,10112],{},[1908,10111,5308],{},[1905,10113,10114,10116],{},[1955,10115,2791],{"mathvariant":2789},[1955,10117,2791],{"mathvariant":2789},[1955,10119,1961],{"stretchy":1960},[1908,10121,8472],{},[1955,10123,2023],{"stretchy":1960},[1905,10125,10126,10132,10134,10136],{},[2783,10127,10128,10130],{},[1908,10129,5308],{},[1955,10131,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,10133,1961],{"stretchy":1960},[1908,10135,8472],{},[1955,10137,2023],{"stretchy":1960},[1955,10139,1957],{},[1908,10141,8472],{},[1955,10143,6212],{},[1908,10145,9839],{},[1955,10147,1961],{"stretchy":1960},[1908,10149,8472],{},[1955,10151,2023],{"stretchy":1960},[1912,10153,10154],{"encoding":1914},"R(w) = -\\frac{w \\cdot u''(w)}{u'(w)} = w \\cdot A(w)",[1889,10156,10158,10185,10353,10372],{"className":10157,"ariaHidden":1919},[1918],[1889,10159,10161,10164,10167,10170,10173,10176,10179,10182],{"className":10160},[1923],[1889,10162],{"className":10163,"style":2057},[1927],[1889,10165,5314],{"className":10166,"style":9718},[1932,1933],[1889,10168,1961],{"className":10169},[2061],[1889,10171,8472],{"className":10172,"style":8687},[1932,1933],[1889,10174,2023],{"className":10175},[2367],[1889,10177],{"className":10178,"style":2043},[2042],[1889,10180,1957],{"className":10181},[2047],[1889,10183],{"className":10184,"style":2043},[2042],[1889,10186,10188,10191,10194,10344,10347,10350],{"className":10187},[1923],[1889,10189],{"className":10190,"style":9923},[1927],[1889,10192,3917],{"className":10193},[1932],[1889,10195,10197,10200,10341],{"className":10196},[1932],[1889,10198],{"className":10199},[2061,6726],[1889,10201,10203],{"className":10202},[6567],[1889,10204,10206,10333],{"className":10205},[2075,2076],[1889,10207,10209,10330],{"className":10208},[2080],[1889,10210,10212,10261,10269],{"className":10211,"style":9945},[2084],[1889,10213,10214,10217],{"style":6742},[1889,10215],{"className":10216,"style":6746},[2092],[1889,10218,10220,10252,10255,10258],{"className":10219},[1932],[1889,10221,10223,10226],{"className":10222},[1932],[1889,10224,5308],{"className":10225},[1932,1933],[1889,10227,10229],{"className":10228},[2071],[1889,10230,10232],{"className":10231},[2075],[1889,10233,10235],{"className":10234},[2080],[1889,10236,10238],{"className":10237,"style":9972},[2084],[1889,10239,10240,10243],{"style":6771},[1889,10241],{"className":10242,"style":2093},[2092],[1889,10244,10246],{"className":10245},[2097,2098,2099,2100],[1889,10247,10249],{"className":10248},[1932,2100],[1889,10250,2791],{"className":10251},[1932,2100],[1889,10253,1961],{"className":10254},[2061],[1889,10256,8472],{"className":10257,"style":8687},[1932,1933],[1889,10259,2023],{"className":10260},[2367],[1889,10262,10263,10266],{"style":6783},[1889,10264],{"className":10265,"style":6746},[2092],[1889,10267],{"className":10268,"style":6791},[6790],[1889,10270,10271,10274],{"style":6794},[1889,10272],{"className":10273,"style":6746},[2092],[1889,10275,10277,10280,10283,10286,10289,10321,10324,10327],{"className":10276},[1932],[1889,10278,8472],{"className":10279,"style":8687},[1932,1933],[1889,10281],{"className":10282,"style":4041},[2042],[1889,10284,6212],{"className":10285},[4045],[1889,10287],{"className":10288,"style":4041},[2042],[1889,10290,10292,10295],{"className":10291},[1932],[1889,10293,5308],{"className":10294},[1932,1933],[1889,10296,10298],{"className":10297},[2071],[1889,10299,10301],{"className":10300},[2075],[1889,10302,10304],{"className":10303},[2080],[1889,10305,10307],{"className":10306,"style":2804},[2084],[1889,10308,10309,10312],{"style":2825},[1889,10310],{"className":10311,"style":2093},[2092],[1889,10313,10315],{"className":10314},[2097,2098,2099,2100],[1889,10316,10318],{"className":10317},[1932,2100],[1889,10319,8176],{"className":10320},[1932,2100],[1889,10322,1961],{"className":10323},[2061],[1889,10325,8472],{"className":10326,"style":8687},[1932,1933],[1889,10328,2023],{"className":10329},[2367],[1889,10331,2108],{"className":10332},[2107],[1889,10334,10336],{"className":10335},[2080],[1889,10337,10339],{"className":10338,"style":10062},[2084],[1889,10340],{},[1889,10342],{"className":10343},[2367,6726],[1889,10345],{"className":10346,"style":2043},[2042],[1889,10348,1957],{"className":10349},[2047],[1889,10351],{"className":10352,"style":2043},[2042],[1889,10354,10356,10360,10363,10366,10369],{"className":10355},[1923],[1889,10357],{"className":10358,"style":10359},[1927],"height:0.4445em;",[1889,10361,8472],{"className":10362,"style":8687},[1932,1933],[1889,10364],{"className":10365,"style":4041},[2042],[1889,10367,6212],{"className":10368},[4045],[1889,10370],{"className":10371,"style":4041},[2042],[1889,10373,10375,10378,10381,10384,10387],{"className":10374},[1923],[1889,10376],{"className":10377,"style":2057},[1927],[1889,10379,9839],{"className":10380},[1932,1933],[1889,10382,1961],{"className":10383},[2061],[1889,10385,8472],{"className":10386,"style":8687},[1932,1933],[1889,10388,2023],{"className":10389},[2367],[1798,10391,10392,2704],{},[1884,10393,10394],{},"经济学含义",[1798,10396,10397,10398,10459,10460,10520],{},"对于小额风险",[1889,10399,10401,10419],{"className":10400},[1892],[1889,10402,10404],{"className":10403},[1896],[1898,10405,10406],{"xmlns":1900},[1902,10407,10408,10416],{},[1905,10409,10410],{},[8476,10411,10412,10414],{"accent":1919},[1908,10413,8480],{},[1955,10415,8483],{},[1912,10417,10418],{"encoding":1914},"\\tilde{\\epsilon}",[1889,10420,10422],{"className":10421,"ariaHidden":1919},[1918],[1889,10423,10425,10428],{"className":10424},[1923],[1889,10426],{"className":10427,"style":8710},[1927],[1889,10429,10431],{"className":10430},[1932,8700],[1889,10432,10434],{"className":10433},[2075],[1889,10435,10437],{"className":10436},[2080],[1889,10438,10440,10448],{"className":10439,"style":8710},[2084],[1889,10441,10442,10445],{"style":8713},[1889,10443],{"className":10444,"style":6746},[2092],[1889,10446,8480],{"className":10447},[1932,1933],[1889,10449,10450,10453],{"style":8722},[1889,10451],{"className":10452,"style":6746},[2092],[1889,10454,10456],{"className":10455,"style":8730},[8729],[1889,10457,8483],{"className":10458},[1932],"（零期望，方差",[1889,10461,10463,10481],{"className":10462},[1892],[1889,10464,10466],{"className":10465},[1896],[1898,10467,10468],{"xmlns":1900},[1902,10469,10470,10478],{},[1905,10471,10472],{},[2783,10473,10474,10476],{},[1908,10475,8626],{},[1969,10477,1990],{},[1912,10479,10480],{"encoding":1914},"\\sigma^2",[1889,10482,10484],{"className":10483,"ariaHidden":1919},[1918],[1889,10485,10487,10491],{"className":10486},[1923],[1889,10488],{"className":10489,"style":10490},[1927],"height:0.8141em;",[1889,10492,10494,10497],{"className":10493},[1932],[1889,10495,8626],{"className":10496,"style":6310},[1932,1933],[1889,10498,10500],{"className":10499},[2071],[1889,10501,10503],{"className":10502},[2075],[1889,10504,10506],{"className":10505},[2080],[1889,10507,10509],{"className":10508,"style":10490},[2084],[1889,10510,10511,10514],{"style":2825},[1889,10512],{"className":10513,"style":2093},[2092],[1889,10515,10517],{"className":10516},[2097,2098,2099,2100],[1889,10518,1990],{"className":10519},[1932,2100],"），风险溢价的近似为：",[1889,10522,10524],{"className":10523},[1938],[1889,10525,10527,10565],{"className":10526},[1892],[1889,10528,10530],{"className":10529},[1896],[1898,10531,10532],{"xmlns":1900,"display":1947},[1902,10533,10534,10562],{},[1905,10535,10536,10538,10540,10542,10548,10550,10552,10554,10556],{},[1908,10537,5314],{},[1908,10539,9682],{},[1955,10541,7183],{},[6567,10543,10544,10546],{},[1969,10545,1971],{},[1969,10547,1990],{},[1908,10549,9839],{},[1955,10551,1961],{"stretchy":1960},[1908,10553,8472],{},[1955,10555,2023],{"stretchy":1960},[2783,10557,10558,10560],{},[1908,10559,8626],{},[1969,10561,1990],{},[1912,10563,10564],{"encoding":1914},"RP \\approx \\frac{1}{2} A(w) \\sigma^2",[1889,10566,10568,10589],{"className":10567,"ariaHidden":1919},[1918],[1889,10569,10571,10574,10577,10580,10583,10586],{"className":10570},[1923],[1889,10572],{"className":10573,"style":1928},[1927],[1889,10575,5314],{"className":10576,"style":9718},[1932,1933],[1889,10578,9682],{"className":10579,"style":9722},[1932,1933],[1889,10581],{"className":10582,"style":2043},[2042],[1889,10584,7183],{"className":10585},[2047],[1889,10587],{"className":10588,"style":2043},[2042],[1889,10590,10592,10596,10658,10661,10664,10667,10670],{"className":10591},[1923],[1889,10593],{"className":10594,"style":10595},[1927],"height:2.0074em;vertical-align:-0.686em;",[1889,10597,10599,10602,10655],{"className":10598},[1932],[1889,10600],{"className":10601},[2061,6726],[1889,10603,10605],{"className":10604},[6567],[1889,10606,10608,10647],{"className":10607},[2075,2076],[1889,10609,10611,10644],{"className":10610},[2080],[1889,10612,10614,10625,10633],{"className":10613,"style":6739},[2084],[1889,10615,10616,10619],{"style":6742},[1889,10617],{"className":10618,"style":6746},[2092],[1889,10620,10622],{"className":10621},[1932],[1889,10623,1990],{"className":10624},[1932],[1889,10626,10627,10630],{"style":6783},[1889,10628],{"className":10629,"style":6746},[2092],[1889,10631],{"className":10632,"style":6791},[6790],[1889,10634,10635,10638],{"style":6794},[1889,10636],{"className":10637,"style":6746},[2092],[1889,10639,10641],{"className":10640},[1932],[1889,10642,1971],{"className":10643},[1932],[1889,10645,2108],{"className":10646},[2107],[1889,10648,10650],{"className":10649},[2080],[1889,10651,10653],{"className":10652,"style":6813},[2084],[1889,10654],{},[1889,10656],{"className":10657},[2367,6726],[1889,10659,9839],{"className":10660},[1932,1933],[1889,10662,1961],{"className":10663},[2061],[1889,10665,8472],{"className":10666,"style":8687},[1932,1933],[1889,10668,2023],{"className":10669},[2367],[1889,10671,10673,10676],{"className":10672},[1932],[1889,10674,8626],{"className":10675,"style":6310},[1932,1933],[1889,10677,10679],{"className":10678},[2071],[1889,10680,10682],{"className":10681},[2075],[1889,10683,10685],{"className":10684},[2080],[1889,10686,10688],{"className":10687,"style":9057},[2084],[1889,10689,10690,10693],{"style":3045},[1889,10691],{"className":10692,"style":2093},[2092],[1889,10694,10696],{"className":10695},[2097,2098,2099,2100],[1889,10697,1990],{"className":10698},[1932,2100],[1798,10700,10701,2704],{},[1884,10702,4126],{},[1805,10704,10705,10752],{},[1808,10706,10707,10751],{},[1889,10708,10710,10730],{"className":10709},[1892],[1889,10711,10713],{"className":10712},[1896],[1898,10714,10715],{"xmlns":1900},[1902,10716,10717,10727],{},[1905,10718,10719,10721,10723,10725],{},[1908,10720,9839],{},[1955,10722,1961],{"stretchy":1960},[1908,10724,8472],{},[1955,10726,2023],{"stretchy":1960},[1912,10728,10729],{"encoding":1914},"A(w)",[1889,10731,10733],{"className":10732,"ariaHidden":1919},[1918],[1889,10734,10736,10739,10742,10745,10748],{"className":10735},[1923],[1889,10737],{"className":10738,"style":2057},[1927],[1889,10740,9839],{"className":10741},[1932,1933],[1889,10743,1961],{"className":10744},[2061],[1889,10746,8472],{"className":10747,"style":8687},[1932,1933],[1889,10749,2023],{"className":10750},[2367],"越大，风险规避程度越高，要求的风险溢价越大",[1808,10753,10754,10798,10799,10835],{},[1889,10755,10757,10777],{"className":10756},[1892],[1889,10758,10760],{"className":10759},[1896],[1898,10761,10762],{"xmlns":1900},[1902,10763,10764,10774],{},[1905,10765,10766,10768,10770,10772],{},[1908,10767,5314],{},[1955,10769,1961],{"stretchy":1960},[1908,10771,8472],{},[1955,10773,2023],{"stretchy":1960},[1912,10775,10776],{"encoding":1914},"R(w)",[1889,10778,10780],{"className":10779,"ariaHidden":1919},[1918],[1889,10781,10783,10786,10789,10792,10795],{"className":10782},[1923],[1889,10784],{"className":10785,"style":2057},[1927],[1889,10787,5314],{"className":10788,"style":9718},[1932,1933],[1889,10790,1961],{"className":10791},[2061],[1889,10793,8472],{"className":10794,"style":8687},[1932,1933],[1889,10796,2023],{"className":10797},[2367],"衡量的是财富变化",[1889,10800,10802,10819],{"className":10801},[1892],[1889,10803,10805],{"className":10804},[1896],[1898,10806,10807],{"xmlns":1900},[1902,10808,10809,10816],{},[1905,10810,10811,10813],{},[1908,10812,1967],{},[1908,10814,10815],{"mathvariant":2789},"%",[1912,10817,10818],{"encoding":1914},"x\\%",[1889,10820,10822],{"className":10821,"ariaHidden":1919},[1918],[1889,10823,10825,10829,10832],{"className":10824},[1923],[1889,10826],{"className":10827,"style":10828},[1927],"height:0.8056em;vertical-align:-0.0556em;",[1889,10830,1967],{"className":10831},[1932,1933],[1889,10833,10815],{"className":10834},[1932],"时风险规避的变化",[1877,10837,10839],{"id":10838},"_24-常见效用函数及其风险测度","2.4 常见效用函数及其风险测度",[10841,10842,10843,10993],"table",{},[10844,10845,10846],"thead",{},[10847,10848,10849,10852,10898,10944,10990],"tr",{},[10850,10851,6193],"th",{},[10850,10853,10854],{},[1889,10855,10857,10877],{"className":10856},[1892],[1889,10858,10860],{"className":10859},[1896],[1898,10861,10862],{"xmlns":1900},[1902,10863,10864,10874],{},[1905,10865,10866,10868,10870,10872],{},[1908,10867,5308],{},[1955,10869,1961],{"stretchy":1960},[1908,10871,8472],{},[1955,10873,2023],{"stretchy":1960},[1912,10875,10876],{"encoding":1914},"u(w)",[1889,10878,10880],{"className":10879,"ariaHidden":1919},[1918],[1889,10881,10883,10886,10889,10892,10895],{"className":10882},[1923],[1889,10884],{"className":10885,"style":2057},[1927],[1889,10887,5308],{"className":10888},[1932,1933],[1889,10890,1961],{"className":10891},[2061],[1889,10893,8472],{"className":10894,"style":8687},[1932,1933],[1889,10896,2023],{"className":10897},[2367],[10850,10899,10900,10901],{},"ARA ",[1889,10902,10904,10923],{"className":10903},[1892],[1889,10905,10907],{"className":10906},[1896],[1898,10908,10909],{"xmlns":1900},[1902,10910,10911,10921],{},[1905,10912,10913,10915,10917,10919],{},[1908,10914,9839],{},[1955,10916,1961],{"stretchy":1960},[1908,10918,8472],{},[1955,10920,2023],{"stretchy":1960},[1912,10922,10729],{"encoding":1914},[1889,10924,10926],{"className":10925,"ariaHidden":1919},[1918],[1889,10927,10929,10932,10935,10938,10941],{"className":10928},[1923],[1889,10930],{"className":10931,"style":2057},[1927],[1889,10933,9839],{"className":10934},[1932,1933],[1889,10936,1961],{"className":10937},[2061],[1889,10939,8472],{"className":10940,"style":8687},[1932,1933],[1889,10942,2023],{"className":10943},[2367],[10850,10945,10946,10947],{},"RRA 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Constant Absolute Risk Aversion（常绝对风险规避）",[1808,11968,11969],{},"CRRA: Constant Relative Risk Aversion（常相对风险规避）",[1808,11971,11972],{},"IARA: Increasing Absolute Risk Aversion（递增绝对风险规避）",[1798,11974,11975,11978,11979,12022,12023,12066],{},[1884,11976,11977],{},"实证证据",": 大多数研究支持",[1889,11980,11982,12001],{"className":11981},[1892],[1889,11983,11985],{"className":11984},[1896],[1898,11986,11987],{"xmlns":1900},[1902,11988,11989,11999],{},[1905,11990,11991,11993,11995,11997],{},[1908,11992,9839],{},[1955,11994,1961],{"stretchy":1960},[1908,11996,8472],{},[1955,11998,2023],{"stretchy":1960},[1912,12000,10729],{"encoding":1914},[1889,12002,12004],{"className":12003,"ariaHidden":1919},[1918],[1889,12005,12007,12010,12013,12016,12019],{"className":12006},[1923],[1889,12008],{"className":12009,"style":2057},[1927],[1889,12011,9839],{"className":12012},[1932,1933],[1889,12014,1961],{"className":12015},[2061],[1889,12017,8472],{"className":12018,"style":8687},[1932,1933],[1889,12020,2023],{"className":12021},[2367],"递减（富人更愿意承担绝对风险），",[1889,12024,12026,12045],{"className":12025},[1892],[1889,12027,12029],{"className":12028},[1896],[1898,12030,12031],{"xmlns":1900},[1902,12032,12033,12043],{},[1905,12034,12035,12037,12039,12041],{},[1908,12036,5314],{},[1955,12038,1961],{"stretchy":1960},[1908,12040,8472],{},[1955,12042,2023],{"stretchy":1960},[1912,12044,10776],{"encoding":1914},[1889,12046,12048],{"className":12047,"ariaHidden":1919},[1918],[1889,12049,12051,12054,12057,12060,12063],{"className":12050},[1923],[1889,12052],{"className":12053,"style":2057},[1927],[1889,12055,5314],{"className":12056,"style":9718},[1932,1933],[1889,12058,1961],{"className":12059},[2061],[1889,12061,8472],{"className":12062,"style":8687},[1932,1933],[1889,12064,2023],{"className":12065},[2367],"大致为常数（相对风险偏好不随财富变化）。",[1877,12068,12070],{"id":12069},"_25-更风险规避的概念","2.5 更风险规避的概念",[1798,12072,12073,12075,12076,12137,12138,12209,12210,2698],{},[1884,12074,7743],{},": 如果对所有赌博",[1889,12077,12079,12097],{"className":12078},[1892],[1889,12080,12082],{"className":12081},[1896],[1898,12083,12084],{"xmlns":1900},[1902,12085,12086,12094],{},[1905,12087,12088],{},[8476,12089,12090,12092],{"accent":1919},[1908,12091,8472],{},[1955,12093,8483],{},[1912,12095,12096],{"encoding":1914},"\\tilde{w}",[1889,12098,12100],{"className":12099,"ariaHidden":1919},[1918],[1889,12101,12103,12106],{"className":12102},[1923],[1889,12104],{"className":12105,"style":8710},[1927],[1889,12107,12109],{"className":12108},[1932,8700],[1889,12110,12112],{"className":12111},[2075],[1889,12113,12115],{"className":12114},[2080],[1889,12116,12118,12126],{"className":12117,"style":8710},[2084],[1889,12119,12120,12123],{"style":8713},[1889,12121],{"className":12122,"style":6746},[2092],[1889,12124,8472],{"className":12125,"style":8687},[1932,1933],[1889,12127,12128,12131],{"style":8722},[1889,12129],{"className":12130,"style":6746},[2092],[1889,12132,12134],{"className":12133,"style":9650},[8729],[1889,12135,8483],{"className":12136},[1932],"和所有",[1889,12139,12141,12159],{"className":12140},[1892],[1889,12142,12144],{"className":12143},[1896],[1898,12145,12146],{"xmlns":1900},[1902,12147,12148,12156],{},[1905,12149,12150],{},[1963,12151,12152,12154],{},[1908,12153,8472],{},[1969,12155,3819],{},[1912,12157,12158],{"encoding":1914},"w_0",[1889,12160,12162],{"className":12161,"ariaHidden":1919},[1918],[1889,12163,12165,12168],{"className":12164},[1923],[1889,12166],{"className":12167,"style":2475},[1927],[1889,12169,12171,12174],{"className":12170},[1932],[1889,12172,8472],{"className":12173,"style":8687},[1932,1933],[1889,12175,12177],{"className":12176},[2071],[1889,12178,12180,12201],{"className":12179},[2075,2076],[1889,12181,12183,12198],{"className":12182},[2080],[1889,12184,12186],{"className":12185,"style":2085},[2084],[1889,12187,12189,12192],{"style":12188},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1889,12190],{"className":12191,"style":2093},[2092],[1889,12193,12195],{"className":12194},[2097,2098,2099,2100],[1889,12196,3819],{"className":12197},[1932,2100],[1889,12199,2108],{"className":12200},[2107],[1889,12202,12204],{"className":12203},[2080],[1889,12205,12207],{"className":12206,"style":2115},[2084],[1889,12208],{},"，个体1都比个体2要求更高的风险溢价，则称个体1比个体2",[1884,12211,12212],{},"更风险规避",[1798,12214,12215,12218,12219,2516,12369,12398,12399,12562,12563,2698],{},[1884,12216,12217],{},"Pratt定理",": 个体1比个体2更风险规避 ⟺ ",[1889,12220,12222,12255],{"className":12221},[1892],[1889,12223,12225],{"className":12224},[1896],[1898,12226,12227],{"xmlns":1900},[1902,12228,12229,12252],{},[1905,12230,12231,12237,12239,12242,12244,12250],{},[1963,12232,12233,12235],{},[1908,12234,5308],{},[1969,12236,1971],{},[1955,12238,1957],{},[1908,12240,12241],{},"f",[1955,12243,1961],{"stretchy":1960},[1963,12245,12246,12248],{},[1908,12247,5308],{},[1969,12249,1990],{},[1955,12251,2023],{"stretchy":1960},[1912,12253,12254],{"encoding":1914},"u_1 = f(u_2)",[1889,12256,12258,12313],{"className":12257,"ariaHidden":1919},[1918],[1889,12259,12261,12264,12304,12307,12310],{"className":12260},[1923],[1889,12262],{"className":12263,"style":2475},[1927],[1889,12265,12267,12270],{"className":12266},[1932],[1889,12268,5308],{"className":12269},[1932,1933],[1889,12271,12273],{"className":12272},[2071],[1889,12274,12276,12296],{"className":12275},[2075,2076],[1889,12277,12279,12293],{"className":12278},[2080],[1889,12280,12282],{"className":12281,"style":2085},[2084],[1889,12283,12284,12287],{"style":2088},[1889,12285],{"className":12286,"style":2093},[2092],[1889,12288,12290],{"className":12289},[2097,2098,2099,2100],[1889,12291,1971],{"className":12292},[1932,2100],[1889,12294,2108],{"className":12295},[2107],[1889,12297,12299],{"className":12298},[2080],[1889,12300,12302],{"className":12301,"style":2115},[2084],[1889,12303],{},[1889,12305],{"className":12306,"style":2043},[2042],[1889,12308,1957],{"className":12309},[2047],[1889,12311],{"className":12312,"style":2043},[2042],[1889,12314,12316,12319,12323,12326,12366],{"className":12315},[1923],[1889,12317],{"className":12318,"style":2057},[1927],[1889,12320,12241],{"className":12321,"style":12322},[1932,1933],"margin-right:0.1076em;",[1889,12324,1961],{"className":12325},[2061],[1889,12327,12329,12332],{"className":12328},[1932],[1889,12330,5308],{"className":12331},[1932,1933],[1889,12333,12335],{"className":12334},[2071],[1889,12336,12338,12358],{"className":12337},[2075,2076],[1889,12339,12341,12355],{"className":12340},[2080],[1889,12342,12344],{"className":12343,"style":2085},[2084],[1889,12345,12346,12349],{"style":2088},[1889,12347],{"className":12348,"style":2093},[2092],[1889,12350,12352],{"className":12351},[2097,2098,2099,2100],[1889,12353,1990],{"className":12354},[1932,2100],[1889,12356,2108],{"className":12357},[2107],[1889,12359,12361],{"className":12360},[2080],[1889,12362,12364],{"className":12363,"style":2115},[2084],[1889,12365],{},[1889,12367,2023],{"className":12368},[2367],[1889,12370,12372,12385],{"className":12371},[1892],[1889,12373,12375],{"className":12374},[1896],[1898,12376,12377],{"xmlns":1900},[1902,12378,12379,12383],{},[1905,12380,12381],{},[1908,12382,12241],{},[1912,12384,12241],{"encoding":1914},[1889,12386,12388],{"className":12387,"ariaHidden":1919},[1918],[1889,12389,12391,12395],{"className":12390},[1923],[1889,12392],{"className":12393,"style":12394},[1927],"height:0.8889em;vertical-align:-0.1944em;",[1889,12396,12241],{"className":12397,"style":12322},[1932,1933],"是凹函数 ⟺ ",[1889,12400,12402,12440],{"className":12401},[1892],[1889,12403,12405],{"className":12404},[1896],[1898,12406,12407],{"xmlns":1900},[1902,12408,12409,12437],{},[1905,12410,12411,12417,12419,12421,12423,12425,12431,12433,12435],{},[1963,12412,12413,12415],{},[1908,12414,9839],{},[1969,12416,1971],{},[1955,12418,1961],{"stretchy":1960},[1908,12420,8472],{},[1955,12422,2023],{"stretchy":1960},[1955,12424,6082],{},[1963,12426,12427,12429],{},[1908,12428,9839],{},[1969,12430,1990],{},[1955,12432,1961],{"stretchy":1960},[1908,12434,8472],{},[1955,12436,2023],{"stretchy":1960},[1912,12438,12439],{"encoding":1914},"A_1(w) \\ge A_2(w)",[1889,12441,12443,12507],{"className":12442,"ariaHidden":1919},[1918],[1889,12444,12446,12449,12489,12492,12495,12498,12501,12504],{"className":12445},[1923],[1889,12447],{"className":12448,"style":2057},[1927],[1889,12450,12452,12455],{"className":12451},[1932],[1889,12453,9839],{"className":12454},[1932,1933],[1889,12456,12458],{"className":12457},[2071],[1889,12459,12461,12481],{"className":12460},[2075,2076],[1889,12462,12464,12478],{"className":12463},[2080],[1889,12465,12467],{"className":12466,"style":2085},[2084],[1889,12468,12469,12472],{"style":2088},[1889,12470],{"className":12471,"style":2093},[2092],[1889,12473,12475],{"className":12474},[2097,2098,2099,2100],[1889,12476,1971],{"className":12477},[1932,2100],[1889,12479,2108],{"className":12480},[2107],[1889,12482,12484],{"className":12483},[2080],[1889,12485,12487],{"className":12486,"style":2115},[2084],[1889,12488],{},[1889,12490,1961],{"className":12491},[2061],[1889,12493,8472],{"className":12494,"style":8687},[1932,1933],[1889,12496,2023],{"className":12497},[2367],[1889,12499],{"className":12500,"style":2043},[2042],[1889,12502,6082],{"className":12503},[2047],[1889,12505],{"className":12506,"style":2043},[2042],[1889,12508,12510,12513,12553,12556,12559],{"className":12509},[1923],[1889,12511],{"className":12512,"style":2057},[1927],[1889,12514,12516,12519],{"className":12515},[1932],[1889,12517,9839],{"className":12518},[1932,1933],[1889,12520,12522],{"className":12521},[2071],[1889,12523,12525,12545],{"className":12524},[2075,2076],[1889,12526,12528,12542],{"className":12527},[2080],[1889,12529,12531],{"className":12530,"style":2085},[2084],[1889,12532,12533,12536],{"style":2088},[1889,12534],{"className":12535,"style":2093},[2092],[1889,12537,12539],{"className":12538},[2097,2098,2099,2100],[1889,12540,1990],{"className":12541},[1932,2100],[1889,12543,2108],{"className":12544},[2107],[1889,12546,12548],{"className":12547},[2080],[1889,12549,12551],{"className":12550,"style":2115},[2084],[1889,12552],{},[1889,12554,1961],{"className":12555},[2061],[1889,12557,8472],{"className":12558,"style":8687},[1932,1933],[1889,12560,2023],{"className":12561},[2367],"对所有",[1889,12564,12566,12579],{"className":12565},[1892],[1889,12567,12569],{"className":12568},[1896],[1898,12570,12571],{"xmlns":1900},[1902,12572,12573,12577],{},[1905,12574,12575],{},[1908,12576,8472],{},[1912,12578,8472],{"encoding":1914},[1889,12580,12582],{"className":12581,"ariaHidden":1919},[1918],[1889,12583,12585,12588],{"className":12584},[1923],[1889,12586],{"className":12587,"style":5332},[1927],[1889,12589,8472],{"className":12590,"style":8687},[1932,1933],[1870,12592],{},[1794,12594,12596],{"id":12595},"_3-保险需求模型","3. 保险需求模型",[1877,12598,12600],{"id":12599},"_31-基本模型设定","3.1 基本模型设定",[1798,12602,12603,2704],{},[1884,12604,12605],{},"情境",[1805,12607,12608,12680,12740],{},[1808,12609,12610,12611],{},"初始财富: ",[1889,12612,12614,12631],{"className":12613},[1892],[1889,12615,12617],{"className":12616},[1896],[1898,12618,12619],{"xmlns":1900},[1902,12620,12621,12629],{},[1905,12622,12623],{},[1963,12624,12625,12627],{},[1908,12626,8472],{},[1969,12628,3819],{},[1912,12630,12158],{"encoding":1914},[1889,12632,12634],{"className":12633,"ariaHidden":1919},[1918],[1889,12635,12637,12640],{"className":12636},[1923],[1889,12638],{"className":12639,"style":2475},[1927],[1889,12641,12643,12646],{"className":12642},[1932],[1889,12644,8472],{"className":12645,"style":8687},[1932,1933],[1889,12647,12649],{"className":12648},[2071],[1889,12650,12652,12672],{"className":12651},[2075,2076],[1889,12653,12655,12669],{"className":12654},[2080],[1889,12656,12658],{"className":12657,"style":2085},[2084],[1889,12659,12660,12663],{"style":12188},[1889,12661],{"className":12662,"style":2093},[2092],[1889,12664,12666],{"className":12665},[2097,2098,2099,2100],[1889,12667,3819],{"className":12668},[1932,2100],[1889,12670,2108],{"className":12671},[2107],[1889,12673,12675],{"className":12674},[2080],[1889,12676,12678],{"className":12677,"style":2115},[2084],[1889,12679],{},[1808,12681,12682,12683,12711,12712],{},"潜在损失: ",[1889,12684,12686,12699],{"className":12685},[1892],[1889,12687,12689],{"className":12688},[1896],[1898,12690,12691],{"xmlns":1900},[1902,12692,12693,12697],{},[1905,12694,12695],{},[1908,12696,1910],{},[1912,12698,1910],{"encoding":1914},[1889,12700,12702],{"className":12701,"ariaHidden":1919},[1918],[1889,12703,12705,12708],{"className":12704},[1923],[1889,12706],{"className":12707,"style":1928},[1927],[1889,12709,1910],{"className":12710},[1932,1933],"，发生概率为",[1889,12713,12715,12728],{"className":12714},[1892],[1889,12716,12718],{"className":12717},[1896],[1898,12719,12720],{"xmlns":1900},[1902,12721,12722,12726],{},[1905,12723,12724],{},[1908,12725,1798],{},[1912,12727,1798],{"encoding":1914},[1889,12729,12731],{"className":12730,"ariaHidden":1919},[1918],[1889,12732,12734,12737],{"className":12733},[1923],[1889,12735],{"className":12736,"style":2402},[1927],[1889,12738,1798],{"className":12739},[1932,1933],[1808,12741,12742,12743,12773,12774,12808,12809,12837],{},"保险公司提供保费率",[1889,12744,12746,12761],{"className":12745},[1892],[1889,12747,12749],{"className":12748},[1896],[1898,12750,12751],{"xmlns":1900},[1902,12752,12753,12758],{},[1905,12754,12755],{},[1908,12756,12757],{},"π",[1912,12759,12760],{"encoding":1914},"\\pi",[1889,12762,12764],{"className":12763,"ariaHidden":1919},[1918],[1889,12765,12767,12770],{"className":12766},[1923],[1889,12768],{"className":12769,"style":5332},[1927],[1889,12771,12757],{"className":12772,"style":6310},[1932,1933],"：支付",[1889,12775,12777,12793],{"className":12776},[1892],[1889,12778,12780],{"className":12779},[1896],[1898,12781,12782],{"xmlns":1900},[1902,12783,12784,12790],{},[1905,12785,12786,12788],{},[1908,12787,12757],{},[1908,12789,1967],{},[1912,12791,12792],{"encoding":1914},"\\pi x",[1889,12794,12796],{"className":12795,"ariaHidden":1919},[1918],[1889,12797,12799,12802,12805],{"className":12798},[1923],[1889,12800],{"className":12801,"style":5332},[1927],[1889,12803,12757],{"className":12804,"style":6310},[1932,1933],[1889,12806,1967],{"className":12807},[1932,1933],"可获得",[1889,12810,12812,12825],{"className":12811},[1892],[1889,12813,12815],{"className":12814},[1896],[1898,12816,12817],{"xmlns":1900},[1902,12818,12819,12823],{},[1905,12820,12821],{},[1908,12822,1967],{},[1912,12824,1967],{"encoding":1914},[1889,12826,12828],{"className":12827,"ariaHidden":1919},[1918],[1889,12829,12831,12834],{"className":12830},[1923],[1889,12832],{"className":12833,"style":5332},[1927],[1889,12835,1967],{"className":12836},[1932,1933],"元赔偿",[1798,12839,12840,12843,12844,12872],{},[1884,12841,12842],{},"决策变量",": 购买多少保险",[1889,12845,12847,12860],{"className":12846},[1892],[1889,12848,12850],{"className":12849},[1896],[1898,12851,12852],{"xmlns":1900},[1902,12853,12854,12858],{},[1905,12855,12856],{},[1908,12857,1967],{},[1912,12859,1967],{"encoding":1914},[1889,12861,12863],{"className":12862,"ariaHidden":1919},[1918],[1889,12864,12866,12869],{"className":12865},[1923],[1889,12867],{"className":12868,"style":5332},[1927],[1889,12870,1967],{"className":12871},[1932,1933],"？",[1798,12874,12875,2704],{},[1884,12876,12877],{},"最终财富",[1805,12879,12880,13034],{},[1808,12881,12882,12883,12935,12936],{},"无损失（概率",[1889,12884,12886,12904],{"className":12885},[1892],[1889,12887,12889],{"className":12888},[1896],[1898,12890,12891],{"xmlns":1900},[1902,12892,12893,12901],{},[1905,12894,12895,12897,12899],{},[1969,12896,1971],{},[1955,12898,3917],{},[1908,12900,1798],{},[1912,12902,12903],{"encoding":1914},"1-p",[1889,12905,12907,12926],{"className":12906,"ariaHidden":1919},[1918],[1889,12908,12910,12914,12917,12920,12923],{"className":12909},[1923],[1889,12911],{"className":12912,"style":12913},[1927],"height:0.7278em;vertical-align:-0.0833em;",[1889,12915,1971],{"className":12916},[1932],[1889,12918],{"className":12919,"style":4041},[2042],[1889,12921,3917],{"className":12922},[4045],[1889,12924],{"className":12925,"style":4041},[2042],[1889,12927,12929,12932],{"className":12928},[1923],[1889,12930],{"className":12931,"style":2402},[1927],[1889,12933,1798],{"className":12934},[1932,1933],"）: ",[1889,12937,12939,12963],{"className":12938},[1892],[1889,12940,12942],{"className":12941},[1896],[1898,12943,12944],{"xmlns":1900},[1902,12945,12946,12960],{},[1905,12947,12948,12954,12956,12958],{},[1963,12949,12950,12952],{},[1908,12951,8472],{},[1969,12953,3819],{},[1955,12955,3917],{},[1908,12957,12757],{},[1908,12959,1967],{},[1912,12961,12962],{"encoding":1914},"w_0 - \\pi x",[1889,12964,12966,13022],{"className":12965,"ariaHidden":1919},[1918],[1889,12967,12969,12973,13013,13016,13019],{"className":12968},[1923],[1889,12970],{"className":12971,"style":12972},[1927],"height:0.7333em;vertical-align:-0.15em;",[1889,12974,12976,12979],{"className":12975},[1932],[1889,12977,8472],{"className":12978,"style":8687},[1932,1933],[1889,12980,12982],{"className":12981},[2071],[1889,12983,12985,13005],{"className":12984},[2075,2076],[1889,12986,12988,13002],{"className":12987},[2080],[1889,12989,12991],{"className":12990,"style":2085},[2084],[1889,12992,12993,12996],{"style":12188},[1889,12994],{"className":12995,"style":2093},[2092],[1889,12997,12999],{"className":12998},[2097,2098,2099,2100],[1889,13000,3819],{"className":13001},[1932,2100],[1889,13003,2108],{"className":13004},[2107],[1889,13006,13008],{"className":13007},[2080],[1889,13009,13011],{"className":13010,"style":2115},[2084],[1889,13012],{},[1889,13014],{"className":13015,"style":4041},[2042],[1889,13017,3917],{"className":13018},[4045],[1889,13020],{"className":13021,"style":4041},[2042],[1889,13023,13025,13028,13031],{"className":13024},[1923],[1889,13026],{"className":13027,"style":5332},[1927],[1889,13029,12757],{"className":13030,"style":6310},[1932,1933],[1889,13032,1967],{"className":13033},[1932,1933],[1808,13035,13036,13037,12935,13065],{},"有损失（概率",[1889,13038,13040,13053],{"className":13039},[1892],[1889,13041,13043],{"className":13042},[1896],[1898,13044,13045],{"xmlns":1900},[1902,13046,13047,13051],{},[1905,13048,13049],{},[1908,13050,1798],{},[1912,13052,1798],{"encoding":1914},[1889,13054,13056],{"className":13055,"ariaHidden":1919},[1918],[1889,13057,13059,13062],{"className":13058},[1923],[1889,13060],{"className":13061,"style":2402},[1927],[1889,13063,1798],{"className":13064},[1932,1933],[1889,13066,13068,13126],{"className":13067},[1892],[1889,13069,13071],{"className":13070},[1896],[1898,13072,13073],{"xmlns":1900},[1902,13074,13075,13123],{},[1905,13076,13077,13083,13085,13087,13089,13091,13093,13095,13097,13099,13105,13107,13109,13111,13113,13115,13117,13119,13121],{},[1963,13078,13079,13081],{},[1908,13080,8472],{},[1969,13082,3819],{},[1955,13084,3917],{},[1908,13086,1910],{},[1955,13088,3917],{},[1908,13090,12757],{},[1908,13092,1967],{},[1955,13094,3910],{},[1908,13096,1967],{},[1955,13098,1957],{},[1963,13100,13101,13103],{},[1908,13102,8472],{},[1969,13104,3819],{},[1955,13106,3917],{},[1908,13108,1910],{},[1955,13110,3910],{},[1955,13112,1961],{"stretchy":1960},[1969,13114,1971],{},[1955,13116,3917],{},[1908,13118,12757],{},[1955,13120,2023],{"stretchy":1960},[1908,13122,1967],{},[1912,13124,13125],{"encoding":1914},"w_0 - L - \\pi x + x = w_0 - L + (1-\\pi)x",[1889,13127,13129,13184,13203,13224,13242,13297,13315,13336],{"className":13128,"ariaHidden":1919},[1918],[1889,13130,13132,13135,13175,13178,13181],{"className":13131},[1923],[1889,13133],{"className":13134,"style":12972},[1927],[1889,13136,13138,13141],{"className":13137},[1932],[1889,13139,8472],{"className":13140,"style":8687},[1932,1933],[1889,13142,13144],{"className":13143},[2071],[1889,13145,13147,13167],{"className":13146},[2075,2076],[1889,13148,13150,13164],{"className":13149},[2080],[1889,13151,13153],{"className":13152,"style":2085},[2084],[1889,13154,13155,13158],{"style":12188},[1889,13156],{"className":13157,"style":2093},[2092],[1889,13159,13161],{"className":13160},[2097,2098,2099,2100],[1889,13162,3819],{"className":13163},[1932,2100],[1889,13165,2108],{"className":13166},[2107],[1889,13168,13170],{"className":13169},[2080],[1889,13171,13173],{"className":13172,"style":2115},[2084],[1889,13174],{},[1889,13176],{"className":13177,"style":4041},[2042],[1889,13179,3917],{"className":13180},[4045],[1889,13182],{"className":13183,"style":4041},[2042],[1889,13185,13187,13191,13194,13197,13200],{"className":13186},[1923],[1889,13188],{"className":13189,"style":13190},[1927],"height:0.7667em;vertical-align:-0.0833em;",[1889,13192,1910],{"className":13193},[1932,1933],[1889,13195],{"className":13196,"style":4041},[2042],[1889,13198,3917],{"className":13199},[4045],[1889,13201],{"className":13202,"style":4041},[2042],[1889,13204,13206,13209,13212,13215,13218,13221],{"className":13205},[1923],[1889,13207],{"className":13208,"style":6326},[1927],[1889,13210,12757],{"className":13211,"style":6310},[1932,1933],[1889,13213,1967],{"className":13214},[1932,1933],[1889,13216],{"className":13217,"style":4041},[2042],[1889,13219,3910],{"className":13220},[4045],[1889,13222],{"className":13223,"style":4041},[2042],[1889,13225,13227,13230,13233,13236,13239],{"className":13226},[1923],[1889,13228],{"className":13229,"style":5332},[1927],[1889,13231,1967],{"className":13232},[1932,1933],[1889,13234],{"className":13235,"style":2043},[2042],[1889,13237,1957],{"className":13238},[2047],[1889,13240],{"className":13241,"style":2043},[2042],[1889,13243,13245,13248,13288,13291,13294],{"className":13244},[1923],[1889,13246],{"className":13247,"style":12972},[1927],[1889,13249,13251,13254],{"className":13250},[1932],[1889,13252,8472],{"className":13253,"style":8687},[1932,1933],[1889,13255,13257],{"className":13256},[2071],[1889,13258,13260,13280],{"className":13259},[2075,2076],[1889,13261,13263,13277],{"className":13262},[2080],[1889,13264,13266],{"className":13265,"style":2085},[2084],[1889,13267,13268,13271],{"style":12188},[1889,13269],{"className":13270,"style":2093},[2092],[1889,13272,13274],{"className":13273},[2097,2098,2099,2100],[1889,13275,3819],{"className":13276},[1932,2100],[1889,13278,2108],{"className":13279},[2107],[1889,13281,13283],{"className":13282},[2080],[1889,13284,13286],{"className":13285,"style":2115},[2084],[1889,13287],{},[1889,13289],{"className":13290,"style":4041},[2042],[1889,13292,3917],{"className":13293},[4045],[1889,13295],{"className":13296,"style":4041},[2042],[1889,13298,13300,13303,13306,13309,13312],{"className":13299},[1923],[1889,13301],{"className":13302,"style":13190},[1927],[1889,13304,1910],{"className":13305},[1932,1933],[1889,13307],{"className":13308,"style":4041},[2042],[1889,13310,3910],{"className":13311},[4045],[1889,13313],{"className":13314,"style":4041},[2042],[1889,13316,13318,13321,13324,13327,13330,13333],{"className":13317},[1923],[1889,13319],{"className":13320,"style":2057},[1927],[1889,13322,1961],{"className":13323},[2061],[1889,13325,1971],{"className":13326},[1932],[1889,13328],{"className":13329,"style":4041},[2042],[1889,13331,3917],{"className":13332},[4045],[1889,13334],{"className":13335,"style":4041},[2042],[1889,13337,13339,13342,13345,13348],{"className":13338},[1923],[1889,13340],{"className":13341,"style":2057},[1927],[1889,13343,12757],{"className":13344,"style":6310},[1932,1933],[1889,13346,2023],{"className":13347},[2367],[1889,13349,1967],{"className":13350},[1932,1933],[1798,13352,13353,2704],{},[1884,13354,13355],{},"优化问题",[1889,13357,13359],{"className":13358},[1938],[1889,13360,13362,13452],{"className":13361},[1892],[1889,13363,13365],{"className":13364},[1896],[1898,13366,13367],{"xmlns":1900,"display":1947},[1902,13368,13369,13449],{},[1905,13370,13371,13383,13385,13387,13389,13391,13393,13395,13397,13399,13405,13407,13409,13411,13413,13415,13417,13419,13421,13423,13429,13431,13433,13435,13437,13439,13441,13443,13445,13447],{},[13372,13373,13374,13381],"munder",{},[1905,13375,13376,13379],{},[1908,13377,13378],{},"max",[1955,13380,7010],{},[1908,13382,1967],{},[2042,13384],{"width":2958},[1955,13386,1961],{"stretchy":1960},[1969,13388,1971],{},[1955,13390,3917],{},[1908,13392,1798],{},[1955,13394,2023],{"stretchy":1960},[1908,13396,5308],{},[1955,13398,1961],{"stretchy":1960},[1963,13400,13401,13403],{},[1908,13402,8472],{},[1969,13404,3819],{},[1955,13406,3917],{},[1908,13408,12757],{},[1908,13410,1967],{},[1955,13412,2023],{"stretchy":1960},[1955,13414,3910],{},[1908,13416,1798],{},[1955,13418,6212],{},[1908,13420,5308],{},[1955,13422,1961],{"stretchy":1960},[1963,13424,13425,13427],{},[1908,13426,8472],{},[1969,13428,3819],{},[1955,13430,3917],{},[1908,13432,1910],{},[1955,13434,3910],{},[1955,13436,1961],{"stretchy":1960},[1969,13438,1971],{},[1955,13440,3917],{},[1908,13442,12757],{},[1955,13444,2023],{"stretchy":1960},[1908,13446,1967],{},[1955,13448,2023],{"stretchy":1960},[1912,13450,13451],{"encoding":1914},"\\max_x \\quad (1-p)u(w_0 - \\pi x) + p \\cdot u(w_0 - L + (1-\\pi)x)",[1889,13453,13455,13526,13593,13617,13636,13697,13715,13736],{"className":13454,"ariaHidden":1919},[1918],[1889,13456,13458,13462,13508,13511,13514,13517,13520,13523],{"className":13457},[1923],[1889,13459],{"className":13460,"style":13461},[1927],"height:1.45em;vertical-align:-0.7em;",[1889,13463,13465],{"className":13464},[2571,5778],[1889,13466,13468,13499],{"className":13467},[2075,2076],[1889,13469,13471,13496],{"className":13470},[2080],[1889,13472,13474,13486],{"className":13473,"style":5332},[2084],[1889,13475,13477,13480],{"style":13476},"top:-2.4em;margin-left:0em;",[1889,13478],{"className":13479,"style":6746},[2092],[1889,13481,13483],{"className":13482},[2097,2098,2099,2100],[1889,13484,1967],{"className":13485},[1932,1933,2100],[1889,13487,13488,13491],{"style":8713},[1889,13489],{"className":13490,"style":6746},[2092],[1889,13492,13493],{},[1889,13494,13378],{"className":13495},[2571],[1889,13497,2108],{"className":13498},[2107],[1889,13500,13502],{"className":13501},[2080],[1889,13503,13506],{"className":13504,"style":13505},[2084],"height:0.7em;",[1889,13507],{},[1889,13509],{"className":13510,"style":3061},[2042],[1889,13512,1961],{"className":13513},[2061],[1889,13515,1971],{"className":13516},[1932],[1889,13518],{"className":13519,"style":4041},[2042],[1889,13521,3917],{"className":13522},[4045],[1889,13524],{"className":13525,"style":4041},[2042],[1889,13527,13529,13532,13535,13538,13541,13544,13584,13587,13590],{"className":13528},[1923],[1889,13530],{"className":13531,"style":2057},[1927],[1889,13533,1798],{"className":13534},[1932,1933],[1889,13536,2023],{"className":13537},[2367],[1889,13539,5308],{"className":13540},[1932,1933],[1889,13542,1961],{"className":13543},[2061],[1889,13545,13547,13550],{"className":13546},[1932],[1889,13548,8472],{"className":13549,"style":8687},[1932,1933],[1889,13551,13553],{"className":13552},[2071],[1889,13554,13556,13576],{"className":13555},[2075,2076],[1889,13557,13559,13573],{"className":13558},[2080],[1889,13560,13562],{"className":13561,"style":2085},[2084],[1889,13563,13564,13567],{"style":12188},[1889,13565],{"className":13566,"style":2093},[2092],[1889,13568,13570],{"className":13569},[2097,2098,2099,2100],[1889,13571,3819],{"className":13572},[1932,2100],[1889,13574,2108],{"className":13575},[2107],[1889,13577,13579],{"className":13578},[2080],[1889,13580,13582],{"className":13581,"style":2115},[2084],[1889,13583],{},[1889,13585],{"className":13586,"style":4041},[2042],[1889,13588,3917],{"className":13589},[4045],[1889,13591],{"className":13592,"style":4041},[2042],[1889,13594,13596,13599,13602,13605,13608,13611,13614],{"className":13595},[1923],[1889,13597],{"className":13598,"style":2057},[1927],[1889,13600,12757],{"className":13601,"style":6310},[1932,1933],[1889,13603,1967],{"className":13604},[1932,1933],[1889,13606,2023],{"className":13607},[2367],[1889,13609],{"className":13610,"style":4041},[2042],[1889,13612,3910],{"className":13613},[4045],[1889,13615],{"className":13616,"style":4041},[2042],[1889,13618,13620,13624,13627,13630,13633],{"className":13619},[1923],[1889,13621],{"className":13622,"style":13623},[1927],"height:0.6389em;vertical-align:-0.1944em;",[1889,13625,1798],{"className":13626},[1932,1933],[1889,13628],{"className":13629,"style":4041},[2042],[1889,13631,6212],{"className":13632},[4045],[1889,13634],{"className":13635,"style":4041},[2042],[1889,13637,13639,13642,13645,13648,13688,13691,13694],{"className":13638},[1923],[1889,13640],{"className":13641,"style":2057},[1927],[1889,13643,5308],{"className":13644},[1932,1933],[1889,13646,1961],{"className":13647},[2061],[1889,13649,13651,13654],{"className":13650},[1932],[1889,13652,8472],{"className":13653,"style":8687},[1932,1933],[1889,13655,13657],{"className":13656},[2071],[1889,13658,13660,13680],{"className":13659},[2075,2076],[1889,13661,13663,13677],{"className":13662},[2080],[1889,13664,13666],{"className":13665,"style":2085},[2084],[1889,13667,13668,13671],{"style":12188},[1889,13669],{"className":13670,"style":2093},[2092],[1889,13672,13674],{"className":13673},[2097,2098,2099,2100],[1889,13675,3819],{"className":13676},[1932,2100],[1889,13678,2108],{"className":13679},[2107],[1889,13681,13683],{"className":13682},[2080],[1889,13684,13686],{"className":13685,"style":2115},[2084],[1889,13687],{},[1889,13689],{"className":13690,"style":4041},[2042],[1889,13692,3917],{"className":13693},[4045],[1889,13695],{"className":13696,"style":4041},[2042],[1889,13698,13700,13703,13706,13709,13712],{"className":13699},[1923],[1889,13701],{"className":13702,"style":13190},[1927],[1889,13704,1910],{"className":13705},[1932,1933],[1889,13707],{"className":13708,"style":4041},[2042],[1889,13710,3910],{"className":13711},[4045],[1889,13713],{"className":13714,"style":4041},[2042],[1889,13716,13718,13721,13724,13727,13730,13733],{"className":13717},[1923],[1889,13719],{"className":13720,"style":2057},[1927],[1889,13722,1961],{"className":13723},[2061],[1889,13725,1971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7],{},[1955,14088,2023],{"stretchy":1960},[1955,14090,1957],{},[2783,14092,14093,14095],{},[1908,14094,5308],{},[1955,14096,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,14098,1961],{"stretchy":1960},[1963,14100,14101,14103],{},[1908,14102,8472],{},[1969,14104,3819],{},[1955,14106,3917],{},[1908,14108,1910],{},[1955,14110,3910],{},[1955,14112,1961],{"stretchy":1960},[1969,14114,1971],{},[1955,14116,3917],{},[1908,14118,12757],{},[1955,14120,2023],{"stretchy":1960},[1908,14122,1967],{},[1955,14124,2023],{"stretchy":1960},[1912,14126,14127],{"encoding":1914},"\\begin{align*}\n&-(1-p)\\pi u'(w_0 - \\pi x) + p(1-\\pi) u'(w_0 - L + (1-\\pi)x) = 0 \\\\\n&\\implies (1-p)p u'(w_0 - \\pi x) = p(1-p) u'(w_0 - L + (1-\\pi)x) \\\\\n&\\implies u'(w_0 - \\pi x) = u'(w_0 - L + (1-\\pi)x)\n\\end{align*}",[1889,14129,14131],{"className":14130,"ariaHidden":1919},[1918],[1889,14132,14134,14138],{"className":14133},[1923],[1889,14135],{"className":14136,"style":14137},[1927],"height:4.2em;vertical-align:-1.85em;",[1889,14139,14141],{"className":14140},[1932],[1889,14142,14144,14197],{"className":14143},[8447],[1889,14145,14147],{"className":14146},[8651],[1889,14148,14150,14188],{"className":14149},[2075,2076],[1889,14151,14153,14185],{"className":14152},[2080],[1889,14154,14157,14167,14176],{"className":14155,"style":14156},[2084],"height:2.35em;",[1889,14158,14160,14164],{"style":14159},"top:-4.35em;",[1889,14161],{"className":14162,"style":14163},[2092],"height:2.84em;",[1889,14165],{"className":14166},[1932],[1889,14168,14170,14173],{"style":14169},"top:-2.85em;",[1889,14171],{"className":14172,"style":14163},[2092],[1889,14174],{"className":14175},[1932],[1889,14177,14179,14182],{"style":14178},"top:-1.35em;",[1889,14180],{"className":14181,"style":14163},[2092],[1889,14183],{"className":14184},[1932],[1889,14186,2108],{"className":14187},[2107],[1889,14189,14191],{"className":14190},[2080],[1889,14192,14195],{"className":14193,"style":14194},[2084],"height:1.85em;",[1889,14196],{},[1889,14198,14200],{"className":14199},[8761],[1889,14201,14203,15070],{"className":14202},[2075,2076],[1889,14204,14206,15067],{"className":14205},[2080],[1889,14207,14209,14515,14815],{"className":14208,"style":14156},[2084],[1889,14210,14212,14215],{"style":14211},"top:-4.51em;",[1889,14213],{"className":14214,"style":6746},[2092],[1889,14216,14218,14221,14224,14227,14230,14233,14236,14239,14242,14245,14248,14251,14254,14286,14289,14329,14332,14335,14338,14341,14344,14347,14350,14353,14356,14359,14362,14365,14368,14371,14374,14377,14380,14412,14415,14455,14458,14461,14464,14467,14470,14473,14476,14479,14482,14485,14488,14491,14494,14497,14500,14503,14506,14509,14512],{"className":14217},[1932],[1889,14219],{"className":14220},[1932],[1889,14222],{"className":14223,"style":4041},[2042],[1889,14225,3917],{"className":14226},[4045],[1889,14228],{"className":14229,"style":4041},[2042],[1889,14231,1961],{"className":14232},[2061],[1889,14234,1971],{"className":14235},[1932],[1889,14237],{"className":14238,"style":4041},[2042],[1889,14240,3917],{"className":14241},[4045],[1889,14243],{"className":14244,"style":4041},[2042],[1889,14246,1798],{"className":14247},[1932,1933],[1889,14249,2023],{"className":14250},[2367],[1889,14252,12757],{"className":14253,"style":6310},[1932,1933],[1889,14255,14257,14260],{"className":14256},[1932],[1889,14258,5308],{"className":14259},[1932,1933],[1889,14261,14263],{"className":14262},[2071],[1889,14264,14266],{"className":14265},[2075],[1889,14267,14269],{"className":14268},[2080],[1889,14270,14272],{"className":14271,"style":3042},[2084],[1889,14273,14274,14277],{"style":3045},[1889,14275],{"className":14276,"style":2093},[2092],[1889,14278,14280],{"className":14279},[2097,2098,2099,2100],[1889,14281,14283],{"className":14282},[1932,2100],[1889,14284,2791],{"className":14285},[1932,2100],[1889,14287,1961],{"className":14288},[2061],[1889,14290,14292,14295],{"className":14291},[1932],[1889,14293,8472],{"className":14294,"style":8687},[1932,1933],[1889,14296,14298],{"className":14297},[2071],[1889,14299,14301,14321],{"className":14300},[2075,2076],[1889,14302,14304,14318],{"className":14303},[2080],[1889,14305,14307],{"className":14306,"style":2085},[2084],[1889,14308,14309,14312],{"style":12188},[1889,14310],{"className":14311,"style":2093},[2092],[1889,14313,14315],{"className":14314},[2097,2098,2099,2100],[1889,14316,3819],{"className":14317},[1932,2100],[1889,14319,2108],{"className":14320},[2107],[1889,14322,14324],{"className":14323},[2080],[1889,14325,14327],{"className":14326,"style":2115},[2084],[1889,14328],{},[1889,14330],{"className":14331,"style":4041},[2042],[1889,14333,3917],{"className":14334},[4045],[1889,14336],{"className":14337,"style":4041},[2042],[1889,14339,12757],{"className":14340,"style":6310},[1932,1933],[1889,14342,1967],{"className":14343},[1932,1933],[1889,14345,2023],{"className":14346},[2367],[1889,14348],{"className":14349,"style":4041},[2042],[1889,14351,3910],{"className":14352},[4045],[1889,14354],{"className":14355,"style":4041},[2042],[1889,14357,1798],{"className":14358},[1932,1933],[1889,14360,1961],{"className":14361},[2061],[1889,14363,1971],{"className":14364},[1932],[1889,14366],{"className":14367,"style":4041},[2042],[1889,14369,3917],{"className":14370},[4045],[1889,14372],{"className":14373,"style":4041},[2042],[1889,14375,12757],{"className":14376,"style":6310},[1932,1933],[1889,14378,2023],{"className":14379},[2367],[1889,14381,14383,14386],{"className":14382},[1932],[1889,14384,5308],{"className":14385},[1932,1933],[1889,14387,14389],{"className":14388},[2071],[1889,14390,14392],{"className":14391},[2075],[1889,14393,14395],{"className":14394},[2080],[1889,14396,14398],{"className":14397,"style":3042},[2084],[1889,14399,144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14957,14959],{"className":14958},[2080],[1889,14960,14962],{"className":14961,"style":3042},[2084],[1889,14963,14964,14967],{"style":3045},[1889,14965],{"className":14966,"style":2093},[2092],[1889,14968,14970],{"className":14969},[2097,2098,2099,2100],[1889,14971,14973],{"className":14972},[1932,2100],[1889,14974,2791],{"className":14975},[1932,2100],[1889,14977,1961],{"className":14978},[2061],[1889,14980,14982,14985],{"className":14981},[1932],[1889,14983,8472],{"className":14984,"style":8687},[1932,1933],[1889,14986,14988],{"className":14987},[2071],[1889,14989,14991,15011],{"className":14990},[2075,2076],[1889,14992,14994,15008],{"className":14993},[2080],[1889,14995,14997],{"className":14996,"style":2085},[2084],[1889,14998,14999,15002],{"style":12188},[1889,15000],{"className":15001,"style":2093},[2092],[1889,15003,15005],{"className":15004},[2097,2098,2099,2100],[1889,15006,3819],{"className":15007},[1932,2100],[1889,15009,2108],{"className":15010},[2107],[1889,15012,15014],{"className":15013},[2080],[1889,15015,15017],{"className":15016,"style":2115},[2084],[1889,15018],{},[1889,15020],{"className":15021,"style":4041},[2042],[1889,15023,3917],{"className":15024},[4045],[1889,15026],{"className":15027,"style":4041},[2042],[1889,15029,1910],{"className":15030},[1932,1933],[1889,15032],{"className":15033,"style":4041},[2042],[1889,15035,3910],{"className":15036},[4045],[1889,15038],{"className":15039,"style":4041},[2042],[1889,15041,1961],{"className":15042},[2061],[1889,15044,1971],{"className":15045},[1932],[1889,15047],{"className":15048,"style":4041},[2042],[1889,15050,3917],{"className":15051},[4045],[1889,15053],{"className":15054,"style":4041},[2042],[1889,15056,12757],{"className":15057,"style":6310},[1932,1933],[1889,15059,2023],{"className":15060},[2367],[1889,15062,1967],{"className":15063},[1932,1933],[1889,15065,2023],{"className":15066},[2367],[1889,15068,2108],{"className":15069},[2107],[1889,15071,15073],{"className":15072},[2080],[1889,15074,15076],{"className":15075,"style":14194},[2084],[1889,15077],{},[1798,15079,15080,15081,15143],{},"由于",[1889,15082,15084,15102],{"className":15083},[1892],[1889,15085,15087],{"className":15086},[1896],[1898,15088,15089],{"xmlns":1900},[1902,15090,15091,15099],{},[1905,15092,15093],{},[2783,15094,15095,15097],{},[1908,15096,5308],{},[1955,15098,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1912,15100,15101],{"encoding":1914},"u'",[1889,15103,15105],{"className":15104,"ariaHidden":1919},[1918],[1889,15106,15108,15111],{"className":15107},[1923],[1889,15109],{"className":15110,"style":2804},[1927],[1889,15112,15114,15117],{"className":15113},[1932],[1889,15115,5308],{"className":15116},[1932,1933],[1889,15118,15120],{"className":15119},[2071],[1889,15121,15123],{"className":15122},[2075],[1889,15124,15126],{"className":15125},[2080],[1889,15127,15129],{"className":15128,"style":2804},[2084],[1889,15130,15131,15134],{"style":2825},[1889,15132],{"className":15133,"style":2093},[2092],[1889,15135,15137],{"className":15136},[2097,2098,2099,2100],[1889,15138,15140],{"className":15139},[1932,2100],[1889,15141,2791],{"className":15142},[1932,2100],"严格递减（凹函数），这意味着：",[1889,15145,15147],{"className":15146},[1938],[1889,15148,15150,15200],{"className":15149},[1892],[1889,15151,15153],{"className":15152},[1896],[1898,15154,15155],{"xmlns":1900,"display":1947},[1902,15156,15157,15197],{},[1905,15158,15159,15165,15167,15169,15171,15173,15179,15181,15183,15185,15187,15189,15191,15193,15195],{},[1963,15160,15161,15163],{},[1908,15162,8472],{},[1969,15164,3819],{},[1955,15166,3917],{},[1908,15168,12757],{},[1908,15170,1967],{},[1955,15172,1957],{},[1963,15174,15175,15177],{},[1908,15176,8472],{},[1969,15178,3819],{},[1955,15180,3917],{},[1908,15182,1910],{},[1955,15184,3910],{},[1955,15186,1961],{"stretchy":1960},[1969,15188,1971],{},[1955,15190,3917],{},[1908,15192,12757],{},[1955,15194,2023],{"stretchy":1960},[1908,15196,1967],{},[1912,15198,15199],{"encoding":1914},"w_0 - \\pi x = w_0 - L + (1-\\pi)x",[1889,15201,15203,15258,15279,15334,15352,15373],{"className":15202,"ariaHidden":1919},[1918],[1889,15204,15206,15209,15249,15252,15255],{"className":15205},[1923],[1889,15207],{"className":15208,"style":12972},[1927],[1889,15210,15212,15215],{"className":15211},[1932],[1889,15213,8472],{"className":15214,"style":8687},[1932,1933],[1889,15216,15218],{"className":15217},[2071],[1889,15219,15221,15241],{"className":15220},[2075,2076],[1889,15222,15224,15238],{"className":15223},[2080],[1889,15225,15227],{"className":15226,"style":2085},[2084],[1889,15228,15229,15232],{"style":12188},[1889,15230],{"className":15231,"style":2093},[2092],[1889,15233,15235],{"className":15234},[2097,2098,2099,2100],[1889,15236,3819],{"className":15237},[1932,2100],[1889,15239,2108],{"className":15240},[2107],[1889,15242,15244],{"className":15243},[2080],[1889,15245,15247],{"className":15246,"style":2115},[2084],[1889,15248],{},[1889,15250],{"className":15251,"style":4041},[2042],[1889,15253,3917],{"className":15254},[4045],[1889,15256],{"className":15257,"style":4041},[2042],[1889,15259,15261,15264,15267,15270,15273,15276],{"className":15260},[1923],[1889,15262],{"className":15263,"style":5332},[1927],[1889,15265,12757],{"className":15266,"style":6310},[1932,1933],[1889,15268,1967],{"className":15269},[1932,1933],[1889,15271],{"className":15272,"style":2043},[2042],[1889,15274,1957],{"className":15275},[2047],[1889,15277],{"className":15278,"style":2043},[2042],[1889,15280,15282,15285,15325,15328,15331],{"className":15281},[1923],[1889,15283],{"className":15284,"style":12972},[1927],[1889,15286,15288,15291],{"className":15287},[1932],[1889,15289,8472],{"className":15290,"style":8687},[1932,1933],[1889,15292,15294],{"className":15293},[2071],[1889,15295,15297,15317],{"className":15296},[2075,2076],[1889,15298,15300,15314],{"className":15299},[2080],[1889,15301,15303],{"className":15302,"style":2085},[2084],[1889,15304,15305,15308],{"style":12188},[1889,15306],{"className":15307,"style":2093},[2092],[1889,15309,15311],{"className":15310},[2097,2098,2099,2100],[1889,15312,3819],{"className":15313},[1932,2100],[1889,15315,2108],{"className":15316},[2107],[1889,15318,15320],{"className":15319},[2080],[1889,15321,15323],{"className":15322,"style":2115},[2084],[1889,15324],{},[1889,15326],{"className":15327,"style":4041},[2042],[1889,15329,3917],{"className":15330},[4045],[1889,15332],{"className":15333,"style":4041},[2042],[1889,15335,15337,15340,15343,15346,15349],{"className":15336},[1923],[1889,15338],{"className":15339,"style":13190},[1927],[1889,15341,1910],{"className":15342},[1932,1933],[1889,15344],{"className":15345,"style":4041},[2042],[1889,15347,3910],{"className":15348},[4045],[1889,15350],{"className":15351,"style":4041},[2042],[1889,15353,15355,15358,15361,15364,15367,15370],{"className":15354},[1923],[1889,15356],{"className":15357,"style":2057},[1927],[1889,15359,1961],{"className":15360},[2061],[1889,15362,1971],{"className":15363},[1932],[1889,15365],{"className":15366,"style":4041},[2042],[1889,15368,3917],{"className":15369},[4045],[1889,15371],{"className":15372,"style":4041},[2042],[1889,15374,15376,15379,15382,15385],{"className":15375},[1923],[1889,15377],{"className":15378,"style":2057},[1927],[1889,15380,12757],{"className":15381,"style":6310},[1932,1933],[1889,15383,2023],{"className":15384},[2367],[1889,15386,1967],{"className":15387},[1932,1933],[1889,15389,15391],{"className":15390},[1938],[1889,15392,15394,15428],{"className":15393},[1892],[1889,15395,15397],{"className":15396},[1896],[1898,15398,15399],{"xmlns":1900,"display":1947},[1902,15400,15401,15425],{},[1905,15402,15403,15405,15407,15409,15411,15413,15415,15417,15419,15421,15423],{},[1908,15404,12757],{},[1908,15406,1967],{},[1955,15408,1957],{},[1908,15410,1910],{},[1955,15412,3917],{},[1955,15414,1961],{"stretchy":1960},[1969,15416,1971],{},[1955,15418,3917],{},[1908,15420,12757],{},[1955,15422,2023],{"stretchy":1960},[1908,15424,1967],{},[1912,15426,15427],{"encoding":1914},"\\pi x = L - (1-\\pi)x",[1889,15429,15431,15452,15470,15491],{"className":15430,"ariaHidden":1919},[1918],[1889,15432,15434,15437,15440,15443,15446,15449],{"className":15433},[1923],[1889,15435],{"className":15436,"style":5332},[1927],[1889,15438,12757],{"className":15439,"style":6310},[1932,1933],[1889,15441,1967],{"className":15442},[1932,1933],[1889,15444],{"className":15445,"style":2043},[2042],[1889,15447,1957],{"className":15448},[2047],[1889,15450],{"className":15451,"style":2043},[2042],[1889,15453,15455,15458,15461,15464,15467],{"className":15454},[1923],[1889,15456],{"className":15457,"style":13190},[1927],[1889,15459,1910],{"className":15460},[1932,1933],[1889,15462],{"className":15463,"style":4041},[2042],[1889,15465,3917],{"className":15466},[4045],[1889,15468],{"className":15469,"style":4041},[2042],[1889,15471,15473,15476,15479,15482,15485,15488],{"className":15472},[1923],[1889,15474],{"className":15475,"style":2057},[1927],[1889,15477,1961],{"className":15478},[2061],[1889,15480,1971],{"className":15481},[1932],[1889,15483],{"className":15484,"style":4041},[2042],[1889,15486,3917],{"className":15487},[4045],[1889,15489],{"className":15490,"style":4041},[2042],[1889,15492,15494,15497,15500,15503],{"className":15493},[1923],[1889,15495],{"className":15496,"style":2057},[1927],[1889,15498,12757],{"className":15499,"style":6310},[1932,1933],[1889,15501,2023],{"className":15502},[2367],[1889,15504,1967],{"className":15505},[1932,1933],[1889,15507,15509],{"className":15508},[1938],[1889,15510,15512,15530],{"className":15511},[1892],[1889,15513,15515],{"className":15514},[1896],[1898,15516,15517],{"xmlns":1900,"display":1947},[1902,15518,15519,15527],{},[1905,15520,15521,15523,15525],{},[1908,15522,1967],{},[1955,15524,1957],{},[1908,15526,1910],{},[1912,15528,15529],{"encoding":1914},"x = L",[1889,15531,15533,15551],{"className":15532,"ariaHidden":1919},[1918],[1889,15534,15536,15539,15542,15545,15548],{"className":15535},[1923],[1889,15537],{"className":15538,"style":5332},[1927],[1889,15540,1967],{"className":15541},[1932,1933],[1889,15543],{"className":15544,"style":2043},[2042],[1889,15546,1957],{"className":15547},[2047],[1889,15549],{"className":15550,"style":2043},[2042],[1889,15552,15554,15557],{"className":15553},[1923],[1889,15555],{"className":15556,"style":1928},[1927],[1889,15558,1910],{"className":15559},[1932,1933],[1798,15561,15562,15565,15566,6352,15569,15652],{},[1884,15563,15564],{},"定理",": 在公平保险下，风险规避的个体会购买",[1884,15567,15568],{},"完全保险",[1889,15570,15572,15595],{"className":15571},[1892],[1889,15573,15575],{"className":15574},[1896],[1898,15576,15577],{"xmlns":1900},[1902,15578,15579,15592],{},[1905,15580,15581,15588,15590],{},[2783,15582,15583,15585],{},[1908,15584,1967],{},[1955,15586,15587],{},"∗",[1955,15589,1957],{},[1908,15591,1910],{},[1912,15593,15594],{"encoding":1914},"x^* = L",[1889,15596,15598,15643],{"className":15597,"ariaHidden":1919},[1918],[1889,15599,15601,15605,15634,15637,15640],{"className":15600},[1923],[1889,15602],{"className":15603,"style":15604},[1927],"height:0.6887em;",[1889,15606,15608,15611],{"className":15607},[1932],[1889,15609,1967],{"className":15610},[1932,1933],[1889,15612,15614],{"className":15613},[2071],[1889,15615,15617],{"className":15616},[2075],[1889,15618,15620],{"className":15619},[2080],[1889,15621,15623],{"className":15622,"style":15604},[2084],[1889,15624,15625,15628],{"style":2825},[1889,15626],{"className":15627,"style":2093},[2092],[1889,15629,15631],{"className":15630},[2097,2098,2099,2100],[1889,15632,15587],{"className":15633},[4045,2100],[1889,15635],{"className":15636,"style":2043},[2042],[1889,15638,1957],{"className":15639},[2047],[1889,15641],{"className":15642,"style":2043},[2042],[1889,15644,15646,15649],{"className":15645},[1923],[1889,15647],{"className":15648,"style":1928},[1927],[1889,15650,1910],{"className":15651},[1932,1933],"），使得无论损失是否发生，最终财富都相同。",[1877,15654,15656],{"id":15655},"_33-非公平保险","3.3 非公平保险",[1798,15658,15659,15660,15711],{},"在现实中，",[1889,15661,15663,15681],{"className":15662},[1892],[1889,15664,15666],{"className":15665},[1896],[1898,15667,15668],{"xmlns":1900},[1902,15669,15670,15678],{},[1905,15671,15672,15674,15676],{},[1908,15673,12757],{},[1955,15675,6369],{},[1908,15677,1798],{},[1912,15679,15680],{"encoding":1914},"\\pi > p",[1889,15682,15684,15702],{"className":15683,"ariaHidden":1919},[1918],[1889,15685,15687,15690,15693,15696,15699],{"className":15686},[1923],[1889,15688],{"className":15689,"style":3838},[1927],[1889,15691,12757],{"className":15692,"style":6310},[1932,1933],[1889,15694],{"className":15695,"style":2043},[2042],[1889,15697,6369],{"className":15698},[2047],[1889,15700],{"className":15701,"style":2043},[2042],[1889,15703,15705,15708],{"className":15704},[1923],[1889,15706],{"className":15707,"style":2402},[1927],[1889,15709,1798],{"className":15710},[1932,1933],"（保险公司需要盈利）。",[1798,15713,15714,2704],{},[1884,15715,15716],{},"命题",[6182,15718,15719,15855,15858],{},[1808,15720,9258,15721,15771,15772,15854],{},[1889,15722,15724,15741],{"className":15723},[1892],[1889,15725,15727],{"className":15726},[1896],[1898,15728,15729],{"xmlns":1900},[1902,15730,15731,15739],{},[1905,15732,15733,15735,15737],{},[1908,15734,12757],{},[1955,15736,6369],{},[1908,15738,1798],{},[1912,15740,15680],{"encoding":1914},[1889,15742,15744,15762],{"className":15743,"ariaHidden":1919},[1918],[1889,15745,15747,15750,15753,15756,15759],{"className":15746},[1923],[1889,15748],{"className":15749,"style":3838},[1927],[1889,15751,12757],{"className":15752,"style":6310},[1932,1933],[1889,15754],{"className":15755,"style":2043},[2042],[1889,15757,6369],{"className":15758},[2047],[1889,15760],{"className":15761,"style":2043},[2042],[1889,15763,15765,15768],{"className":15764},[1923],[1889,15766],{"className":15767,"style":2402},[1927],[1889,15769,1798],{"className":15770},[1932,1933],"，风险规避者会购买部分保险（",[1889,15773,15775,15797],{"className":15774},[1892],[1889,15776,15778],{"className":15777},[1896],[1898,15779,15780],{"xmlns":1900},[1902,15781,15782,15794],{},[1905,15783,15784,15790,15792],{},[2783,15785,15786,15788],{},[1908,15787,1967],{},[1955,15789,15587],{},[1955,15791,8012],{},[1908,15793,1910],{},[1912,15795,15796],{"encoding":1914},"x^* \u003C L",[1889,15798,15800,15845],{"className":15799,"ariaHidden":1919},[1918],[1889,15801,15803,15807,15836,15839,15842],{"className":15802},[1923],[1889,15804],{"className":15805,"style":15806},[1927],"height:0.7278em;vertical-align:-0.0391em;",[1889,15808,15810,15813],{"className":15809},[1932],[1889,15811,1967],{"className":15812},[1932,1933],[1889,15814,15816],{"className":15815},[2071],[1889,15817,15819],{"className":15818},[2075],[1889,15820,15822],{"className":15821},[2080],[1889,15823,15825],{"className":15824,"style":15604},[2084],[1889,15826,15827,15830],{"style":2825},[1889,15828],{"className":15829,"style":2093},[2092],[1889,15831,15833],{"className":15832},[2097,2098,2099,2100],[1889,15834,15587],{"className":15835},[4045,2100],[1889,15837],{"className":15838,"style":2043},[2042],[1889,15840,8012],{"className":15841},[2047],[1889,15843],{"className":15844,"style":2043},[2042],[1889,15846,15848,15851],{"className":15847},[1923],[1889,15849],{"className":15850,"style":1928},[1927],[1889,15852,1910],{"className":15853},[1932,1933],"）",[1808,15856,15857],{},"风险规避程度越高，购买的保险越多",[1808,15859,15860,15861,15925],{},"存在临界保费率",[1889,15862,15864,15883],{"className":15863},[1892],[1889,15865,15867],{"className":15866},[1896],[1898,15868,15869],{"xmlns":1900},[1902,15870,15871,15880],{},[1905,15872,15873],{},[8476,15874,15875,15877],{"accent":1919},[1908,15876,12757],{},[1955,15878,15879],{},"ˉ",[1912,15881,15882],{"encoding":1914},"\\bar{\\pi}",[1889,15884,15886],{"className":15885,"ariaHidden":1919},[1918],[1889,15887,15889,15893],{"className":15888},[1923],[1889,15890],{"className":15891,"style":15892},[1927],"height:0.5678em;",[1889,15894,15896],{"className":15895},[1932,8700],[1889,15897,15899],{"className":15898},[2075],[1889,15900,15902],{"className":15901},[2080],[1889,15903,15905,15913],{"className":15904,"style":15892},[2084],[1889,15906,15907,15910],{"style":8713},[1889,15908],{"className":15909,"style":6746},[2092],[1889,15911,12757],{"className":15912,"style":6310},[1932,1933],[1889,15914,15915,15918],{"style":8713},[1889,15916],{"className":15917,"style":6746},[2092],[1889,15919,15922],{"className":15920,"style":15921},[8729],"left:-0.25em;",[1889,15923,15879],{"className":15924},[1932],"，超过此值则完全不购买保险",[1798,15927,15928,2704],{},[1884,15929,15930],{},"数值例子",[1798,15932,15933,15934,16017,16018,16017,16111,16017,16163,16017,16215,2698],{},"设",[1889,15935,15937,15969],{"className":15936},[1892],[1889,15938,15940],{"className":15939},[1896],[1898,15941,15942],{"xmlns":1900},[1902,15943,15944,15966],{},[1905,15945,15946,15948,15950,15952,15954,15956,15958,15960,15962,15964],{},[1908,15947,5308],{},[1955,15949,1961],{"stretchy":1960},[1908,15951,8472],{},[1955,15953,2023],{"stretchy":1960},[1955,15955,1957],{},[1908,15957,7007],{},[1955,15959,7010],{},[1955,15961,1961],{"stretchy":1960},[1908,15963,8472],{},[1955,15965,2023],{"stretchy":1960},[1912,15967,15968],{"encoding":1914},"u(w) = \\ln(w)",[1889,15970,15972,15999],{"className":15971,"ariaHidden":1919},[1918],[1889,15973,15975,15978,15981,15984,15987,15990,15993,15996],{"className":15974},[1923],[1889,15976],{"className":15977,"style":2057},[1927],[1889,15979,5308],{"className":15980},[1932,1933],[1889,15982,1961],{"className":15983},[2061],[1889,15985,8472],{"className":15986,"style":8687},[1932,1933],[1889,15988,2023],{"className":15989},[2367],[1889,15991],{"className":15992,"style":2043},[2042],[1889,15994,1957],{"className":15995},[2047],[1889,15997],{"className":15998,"style":2043},[2042],[1889,16000,16002,16005,16008,16011,16014],{"className":16001},[1923],[1889,16003],{"className":16004,"style":2057},[1927],[1889,16006,7007],{"className":16007},[2571],[1889,16009,1961],{"className":16010},[2061],[1889,16012,8472],{"className":16013,"style":8687},[1932,1933],[1889,16015,2023],{"className":16016},[2367],"，",[1889,16019,16021,16044],{"className":16020},[1892],[1889,16022,16024],{"className":16023},[1896],[1898,16025,16026],{"xmlns":1900},[1902,16027,16028,16041],{},[1905,16029,16030,16036,16038],{},[1963,16031,16032,16034],{},[1908,16033,8472],{},[1969,16035,3819],{},[1955,16037,1957],{},[1969,16039,16040],{},"100",[1912,16042,16043],{"encoding":1914},"w_0 = 100",[1889,16045,16047,16102],{"className":16046,"ariaHidden":1919},[1918],[1889,16048,16050,16053,16093,16096,16099],{"className":16049},[1923],[1889,16051],{"className":16052,"style":2475},[1927],[1889,16054,16056,16059],{"className":16055},[1932],[1889,16057,8472],{"className":16058,"style":8687},[1932,1933],[1889,16060,16062],{"className":16061},[2071],[1889,16063,16065,16085],{"className":16064},[2075,2076],[1889,16066,16068,16082],{"className":16067},[2080],[1889,16069,16071],{"className":16070,"style":2085},[2084],[1889,16072,16073,16076],{"style":12188},[1889,16074],{"className":16075,"style":2093},[2092],[1889,16077,16079],{"className":16078},[2097,2098,2099,2100],[1889,16080,3819],{"className":16081},[1932,2100],[1889,16083,2108],{"className":16084},[2107],[1889,16086,16088],{"className":16087},[2080],[1889,16089,16091],{"className":16090,"style":2115},[2084],[1889,16092],{},[1889,16094],{"className":16095,"style":2043},[2042],[1889,16097,1957],{"className":16098},[2047],[1889,16100],{"className":16101,"style":2043},[2042],[1889,16103,16105,16108],{"className":16104},[1923],[1889,16106],{"className":16107,"style":2694},[1927],[1889,16109,16040],{"className":16110},[1932],[1889,16112,16114,16133],{"className":16113},[1892],[1889,16115,16117],{"className":16116},[1896],[1898,16118,16119],{"xmlns":1900},[1902,16120,16121,16130],{},[1905,16122,16123,16125,16127],{},[1908,16124,1910],{},[1955,16126,1957],{},[1969,16128,16129],{},"36",[1912,16131,16132],{"encoding":1914},"L = 36",[1889,16134,16136,16154],{"className":16135,"ariaHidden":1919},[1918],[1889,16137,16139,16142,16145,16148,16151],{"className":16138},[1923],[1889,16140],{"className":16141,"style":1928},[1927],[1889,16143,1910],{"className":16144},[1932,1933],[1889,16146],{"className":16147,"style":2043},[2042],[1889,16149,1957],{"className":16150},[2047],[1889,16152],{"className":16153,"style":2043},[2042],[1889,16155,16157,16160],{"className":16156},[1923],[1889,16158],{"className":16159,"style":2694},[1927],[1889,16161,16129],{"className":16162},[1932],[1889,16164,16166,16185],{"className":16165},[1892],[1889,16167,16169],{"className":16168},[1896],[1898,16170,16171],{"xmlns":1900},[1902,16172,16173,16182],{},[1905,16174,16175,16177,16179],{},[1908,16176,1798],{},[1955,16178,1957],{},[1969,16180,16181],{},"0.25",[1912,16183,16184],{"encoding":1914},"p = 0.25",[1889,16186,16188,16206],{"className":16187,"ariaHidden":1919},[1918],[1889,16189,16191,16194,16197,16200,16203],{"className":16190},[1923],[1889,16192],{"className":16193,"style":2402},[1927],[1889,16195,1798],{"className":16196},[1932,1933],[1889,16198],{"className":16199,"style":2043},[2042],[1889,16201,1957],{"className":16202},[2047],[1889,16204],{"className":16205,"style":2043},[2042],[1889,16207,16209,16212],{"className":16208},[1923],[1889,16210],{"className":16211,"style":2694},[1927],[1889,16213,16181],{"className":16214},[1932],[1889,16216,16218,16237],{"className":16217},[1892],[1889,16219,16221],{"className":16220},[1896],[1898,16222,16223],{"xmlns":1900},[1902,16224,16225,16234],{},[1905,16226,16227,16229,16231],{},[1908,16228,12757],{},[1955,16230,1957],{},[1969,16232,16233],{},"0.4",[1912,16235,16236],{"encoding":1914},"\\pi = 0.4",[1889,16238,16240,16258],{"className":16239,"ariaHidden":1919},[1918],[1889,16241,16243,16246,16249,16252,16255],{"className":16242},[1923],[1889,16244],{"className":16245,"style":5332},[1927],[1889,16247,12757],{"className":16248,"style":6310},[1932,1933],[1889,16250],{"className":16251,"style":2043},[2042],[1889,16253,1957],{"className":16254},[2047],[1889,16256],{"className":16257,"style":2043},[2042],[1889,16259,16261,16264],{"className":16260},[1923],[1889,16262],{"className":16263,"style":2694},[1927],[1889,16265,16233],{"className":16266},[1932],[1798,16268,16269],{},"一阶条件：",[1889,16271,16273],{"className":16272},[1938],[1889,16274,16276,16334],{"className":16275},[1892],[1889,16277,16279],{"className":16278},[1896],[1898,16280,16281],{"xmlns":1900,"display":1947},[1902,16282,16283,16331],{},[1905,16284,16285,16307,16309],{},[6567,16286,16287,16297],{},[1905,16288,16289,16292,16295],{},[1969,16290,16291],{},"0.75",[1955,16293,16294],{},"×",[1969,16296,16233],{},[1905,16298,16299,16301,16303,16305],{},[1969,16300,16040],{},[1955,16302,3917],{},[1969,16304,16233],{},[1908,16306,1967],{},[1955,16308,1957],{},[6567,16310,16311,16320],{},[1905,16312,16313,16315,16317],{},[1969,16314,16181],{},[1955,16316,16294],{},[1969,16318,16319],{},"0.6",[1905,16321,16322,16325,16327,16329],{},[1969,16323,16324],{},"64",[1955,16326,3910],{},[1969,16328,16319],{},[1908,16330,1967],{},[1912,16332,16333],{"encoding":1914},"\\frac{0.75 \\times 0.4}{100 - 0.4x} = \\frac{0.25 \\times 0.6}{64 + 0.6x}",[1889,16335,16337,16443],{"className":16336,"ariaHidden":1919},[1918],[1889,16338,16340,16344,16434,16437,16440],{"className":16339},[1923],[1889,16341],{"className":16342,"style":16343},[1927],"height:2.0908em;vertical-align:-0.7693em;",[1889,16345,16347,16350,16431],{"className":16346},[1932],[1889,16348],{"className":16349},[2061,6726],[1889,16351,16353],{"className":16352},[6567],[1889,16354,16356,16422],{"className":16355},[2075,2076],[1889,16357,16359,16419],{"className":16358},[2080],[1889,16360,16362,16388,16396],{"className":16361,"style":6739},[2084],[1889,16363,16364,16367],{"style":6742},[1889,16365],{"className":16366,"style":6746},[2092],[1889,16368,16370,16373,16376,16379,16382,16385],{"className":16369},[1932],[1889,16371,16040],{"className":16372},[1932],[1889,16374],{"className":16375,"style":4041},[2042],[1889,16377,3917],{"className":16378},[4045],[1889,16380],{"className":16381,"style":4041},[2042],[1889,16383,16233],{"className":16384},[1932],[1889,16386,1967],{"className":16387},[1932,1933],[1889,16389,16390,16393],{"style":6783},[1889,16391],{"className":16392,"style":6746},[2092],[1889,16394],{"className":16395,"style":6791},[6790],[1889,16397,16398,16401],{"style":6794},[1889,16399],{"className":16400,"style":6746},[2092],[1889,16402,16404,16407,16410,16413,16416],{"className":16403},[1932],[1889,16405,16291],{"className":16406},[1932],[1889,16408],{"className":16409,"style":4041},[2042],[1889,16411,16294],{"className":16412},[4045],[1889,16414],{"className":16415,"style":4041},[2042],[1889,16417,16233],{"className":16418},[1932],[1889,16420,2108],{"className":16421},[2107],[1889,16423,16425],{"className":16424},[2080],[1889,16426,16429],{"className":16427,"style":16428},[2084],"height:0.7693em;",[1889,16430],{},[1889,16432],{"className":16433},[2367,6726],[1889,16435],{"className":16436,"style":2043},[2042],[1889,16438,1957],{"className":16439},[2047],[1889,16441],{"className":16442,"style":2043},[2042],[1889,16444,16446,16449],{"className":16445},[1923],[1889,16447],{"className":16448,"style":16343},[1927],[1889,16450,16452,16455,16535],{"className":16451},[1932],[1889,16453],{"className":16454},[2061,6726],[1889,16456,16458],{"className":16457},[6567],[1889,16459,16461,16527],{"className":16460},[2075,2076],[1889,16462,16464,16524],{"className":16463},[2080],[1889,16465,16467,16493,16501],{"className":16466,"style":6739},[2084],[1889,16468,16469,16472],{"style":6742},[1889,16470],{"className":16471,"style":6746},[2092],[1889,16473,16475,16478,16481,16484,16487,16490],{"className":16474},[1932],[1889,16476,16324],{"className":16477},[1932],[1889,16479],{"className":16480,"style":4041},[2042],[1889,16482,3910],{"className":16483},[4045],[1889,16485],{"className":16486,"style":4041},[2042],[1889,16488,16319],{"className":16489},[1932],[1889,16491,1967],{"className":16492},[1932,1933],[1889,16494,16495,16498],{"style":6783},[1889,16496],{"className":16497,"style":6746},[2092],[1889,16499],{"className":16500,"style":6791},[6790],[1889,16502,16503,16506],{"style":6794},[1889,16504],{"className":16505,"style":6746},[2092],[1889,16507,16509,16512,16515,16518,16521],{"className":16508},[1932],[1889,16510,16181],{"className":16511},[1932],[1889,16513],{"className":16514,"style":4041},[2042],[1889,16516,16294],{"className":16517},[4045],[1889,16519],{"className":16520,"style":4041},[2042],[1889,16522,16319],{"className":16523},[1932],[1889,16525,2108],{"className":16526},[2107],[1889,16528,16530],{"className":16529},[2080],[1889,16531,16533],{"className":16532,"style":16428},[2084],[1889,16534],{},[1889,16536],{"className":16537},[2367,6726],[1798,16539,16540,16541,16623,16624,16675],{},"解得",[1889,16542,16544,16567],{"className":16543},[1892],[1889,16545,16547],{"className":16546},[1896],[1898,16548,16549],{"xmlns":1900},[1902,16550,16551,16564],{},[1905,16552,16553,16559,16561],{},[2783,16554,16555,16557],{},[1908,16556,1967],{},[1955,16558,15587],{},[1955,16560,7183],{},[1969,16562,16563],{},"24",[1912,16565,16566],{"encoding":1914},"x^* \\approx 24",[1889,16568,16570,16614],{"className":16569,"ariaHidden":1919},[1918],[1889,16571,16573,16576,16605,16608,16611],{"className":16572},[1923],[1889,16574],{"className":16575,"style":15604},[1927],[1889,16577,16579,16582],{"className":16578},[1932],[1889,16580,1967],{"className":16581},[1932,1933],[1889,16583,16585],{"className":16584},[2071],[1889,16586,16588],{"className":16587},[2075],[1889,16589,16591],{"className":16590},[2080],[1889,16592,16594],{"className":16593,"style":15604},[2084],[1889,16595,16596,16599],{"style":2825},[1889,16597],{"className":16598,"style":2093},[2092],[1889,16600,16602],{"className":16601},[2097,2098,2099,2100],[1889,16603,15587],{"className":16604},[4045,2100],[1889,16606],{"className":16607,"style":2043},[2042],[1889,16609,7183],{"className":16610},[2047],[1889,16612],{"className":16613,"style":2043},[2042],[1889,16615,16617,16620],{"className":16616},[1923],[1889,16618],{"className":16619,"style":2694},[1927],[1889,16621,16563],{"className":16622},[1932],"（部分保险，而非完全保险",[1889,16625,16627,16645],{"className":16626},[1892],[1889,16628,16630],{"className":16629},[1896],[1898,16631,16632],{"xmlns":1900},[1902,16633,16634,16642],{},[1905,16635,16636,16638,16640],{},[1908,16637,1910],{},[1955,16639,1957],{},[1969,16641,16129],{},[1912,16643,16644],{"encoding":1914},"L=36",[1889,16646,16648,16666],{"className":16647,"ariaHidden":1919},[1918],[1889,16649,16651,16654,16657,16660,16663],{"className":16650},[1923],[1889,16652],{"className":16653,"style":1928},[1927],[1889,16655,1910],{"className":16656},[1932,1933],[1889,16658],{"className":16659,"style":2043},[2042],[1889,16661,1957],{"className":16662},[2047],[1889,16664],{"className":16665,"style":2043},[2042],[1889,16667,16669,16672],{"className":16668},[1923],[1889,16670],{"className":16671,"style":2694},[1927],[1889,16673,16129],{"className":16674},[1932],"）。",[1877,16677,16679],{"id":16678},"_34-自负额与共保","3.4 自负额与共保",[1798,16681,16682,16685,16686,16716],{},[1884,16683,16684],{},"自负额 (Deductible)",": 损失的前",[1889,16687,16689,16703],{"className":16688},[1892],[1889,16690,16692],{"className":16691},[1896],[1898,16693,16694],{"xmlns":1900},[1902,16695,16696,16701],{},[1905,16697,16698],{},[1908,16699,16700],{},"D",[1912,16702,16700],{"encoding":1914},[1889,16704,16706],{"className":16705,"ariaHidden":1919},[1918],[1889,16707,16709,16712],{"className":16708},[1923],[1889,16710],{"className":16711,"style":1928},[1927],[1889,16713,16700],{"className":16714,"style":16715},[1932,1933],"margin-right:0.0278em;","元由被保险人承担。",[1798,16718,16719,16722,16723,16751,16752,16675],{},[1884,16720,16721],{},"共保 (Coinsurance)",": 保险公司只赔偿损失的",[1889,16724,16726,16739],{"className":16725},[1892],[1889,16727,16729],{"className":16728},[1896],[1898,16730,16731],{"xmlns":1900},[1902,16732,16733,16737],{},[1905,16734,16735],{},[1908,16736,3811],{},[1912,16738,11242],{"encoding":1914},[1889,16740,16742],{"className":16741,"ariaHidden":1919},[1918],[1889,16743,16745,16748],{"className":16744},[1923],[1889,16746],{"className":16747,"style":5332},[1927],[1889,16749,3811],{"className":16750,"style":3842},[1932,1933],"比例（",[1889,16753,16755,16777],{"className":16754},[1892],[1889,16756,16758],{"className":16757},[1896],[1898,16759,16760],{"xmlns":1900},[1902,16761,16762,16774],{},[1905,16763,16764,16766,16768,16770,16772],{},[1969,16765,3819],{},[1955,16767,8012],{},[1908,16769,3811],{},[1955,16771,8012],{},[1969,16773,1971],{},[1912,16775,16776],{"encoding":1914},"0 \u003C \\alpha \u003C 1",[1889,16778,16780,16799,16817],{"className":16779,"ariaHidden":1919},[1918],[1889,16781,16783,16787,16790,16793,16796],{"className":16782},[1923],[1889,16784],{"className":16785,"style":16786},[1927],"height:0.6835em;vertical-align:-0.0391em;",[1889,16788,3819],{"className":16789},[1932],[1889,16791],{"className":16792,"style":2043},[2042],[1889,16794,8012],{"className":16795},[2047],[1889,16797],{"className":16798,"style":2043},[2042],[1889,16800,16802,16805,16808,16811,16814],{"className":16801},[1923],[1889,16803],{"className":16804,"style":3838},[1927],[1889,16806,3811],{"className":16807,"style":3842},[1932,1933],[1889,16809],{"className":16810,"style":2043},[2042],[1889,16812,8012],{"className":16813},[2047],[1889,16815],{"className":16816,"style":2043},[2042],[1889,16818,16820,16823],{"className":16819},[1923],[1889,16821],{"className":16822,"style":2694},[1927],[1889,16824,1971],{"className":16825},[1932],[1798,16827,16828],{},[1884,16829,16830],{},"为什么保险公司使用这些机制？",[6182,16832,16833,16839,16845],{},[1808,16834,16835,16838],{},[1884,16836,16837],{},"降低道德风险",": 让被保险人分担部分损失，激励其小心",[1808,16840,16841,16844],{},[1884,16842,16843],{},"吸引低风险客户",": 自负额作为筛选机制（下一章详述）",[1808,16846,16847,16850],{},[1884,16848,16849],{},"降低管理成本",": 小额索赔不值得处理",[1870,16852],{},[1794,16854,16856],{"id":16855},"_4-资产组合选择理论","4. 资产组合选择理论",[1877,16858,16860],{"id":16859},"_41-两资产模型","4.1 两资产模型",[1798,16862,16863,2704],{},[1884,16864,16865],{},"设定",[1805,16867,16868,16946,17169],{},[1808,16869,16870,16871],{},"无风险资产：收益率",[1889,16872,16874,16893],{"className":16873},[1892],[1889,16875,16877],{"className":16876},[1896],[1898,16878,16879],{"xmlns":1900},[1902,16880,16881,16890],{},[1905,16882,16883],{},[1963,16884,16885,16888],{},[1908,16886,16887],{},"r",[1908,16889,12241],{},[1912,16891,16892],{"encoding":1914},"r_f",[1889,16894,16896],{"className":16895,"ariaHidden":1919},[1918],[1889,16897,16899,16903],{"className":16898},[1923],[1889,16900],{"className":16901,"style":16902},[1927],"height:0.7167em;vertical-align:-0.2861em;",[1889,16904,16906,16909],{"className":16905},[1932],[1889,16907,16887],{"className":16908,"style":16715},[1932,1933],[1889,16910,16912],{"className":16911},[2071],[1889,16913,16915,16937],{"className":16914},[2075,2076],[1889,16916,16918,16934],{"className":16917},[2080],[1889,16919,16922],{"className":16920,"style":16921},[2084],"height:0.3361em;",[1889,16923,16925,16928],{"style":16924},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1889,16926],{"className":16927,"style":2093},[2092],[1889,16929,16931],{"className":16930},[2097,2098,2099,2100],[1889,16932,12241],{"className":16933,"style":12322},[1932,1933,2100],[1889,16935,2108],{"className":16936},[2107],[1889,16938,16940],{"className":16939},[2080],[1889,16941,16944],{"className":16942,"style":16943},[2084],"height:0.2861em;",[1889,16945],{},[1808,16947,16948,16949,17010,17011,17110,17111],{},"风险资产：随机收益率",[1889,16950,16952,16970],{"className":16951},[1892],[1889,16953,16955],{"className":16954},[1896],[1898,16956,16957],{"xmlns":1900},[1902,16958,16959,16967],{},[1905,16960,16961],{},[8476,16962,16963,16965],{"accent":1919},[1908,16964,16887],{},[1955,16966,8483],{},[1912,16968,16969],{"encoding":1914},"\\tilde{r}",[1889,16971,16973],{"className":16972,"ariaHidden":1919},[1918],[1889,16974,16976,16979],{"className":16975},[1923],[1889,16977],{"className":16978,"style":8710},[1927],[1889,16980,16982],{"className":16981},[1932,8700],[1889,16983,16985],{"className":16984},[2075],[1889,16986,16988],{"className":16987},[2080],[1889,16989,16991,16999],{"className":16990,"style":8710},[2084],[1889,16992,16993,16996],{"style":8713},[1889,16994],{"className":16995,"style":6746},[2092],[1889,16997,16887],{"className":16998,"style":16715},[1932,1933],[1889,17000,17001,17004],{"style":8722},[1889,17002],{"className":17003,"style":6746},[2092],[1889,17005,17007],{"className":17006,"style":8730},[8729],[1889,17008,8483],{"className":17009},[1932],"，期望",[1889,17012,17014,17043],{"className":17013},[1892],[1889,17015,17017],{"className":17016},[1896],[1898,17018,17019],{"xmlns":1900},[1902,17020,17021,17040],{},[1905,17022,17023,17026,17028,17030,17032,17038],{},[1908,17024,17025],{},"μ",[1955,17027,1957],{},[1908,17029,5719],{"mathvariant":5313},[1955,17031,5722],{"stretchy":1960},[8476,17033,17034,17036],{"accent":1919},[1908,17035,16887],{},[1955,17037,8483],{},[1955,17039,5733],{"stretchy":1960},[1912,17041,17042],{"encoding":1914},"\\mu = \\mathbb{E}[\\tilde{r}]",[1889,17044,17046,17064],{"className":17045,"ariaHidden":1919},[1918],[1889,17047,17049,17052,17055,17058,17061],{"className":17048},[1923],[1889,17050],{"className":17051,"style":2402},[1927],[1889,17053,17025],{"className":17054},[1932,1933],[1889,17056],{"className":17057,"style":2043},[2042],[1889,17059,1957],{"className":17060},[2047],[1889,17062],{"className":17063,"style":2043},[2042],[1889,17065,17067,17070,17073,17076,17107],{"className":17066},[1923],[1889,17068],{"className":17069,"style":2057},[1927],[1889,17071,5719],{"className":17072},[1932,5355],[1889,17074,5722],{"className":17075},[2061],[1889,17077,17079],{"className":17078},[1932,8700],[1889,17080,17082],{"className":17081},[2075],[1889,17083,17085],{"className":17084},[2080],[1889,17086,17088,17096],{"className":17087,"style":8710},[2084],[1889,17089,17090,17093],{"style":8713},[1889,17091],{"className":17092,"style":6746},[2092],[1889,17094,16887],{"className":17095,"style":16715},[1932,1933],[1889,17097,17098,17101],{"style":8722},[1889,17099],{"className":17100,"style":6746},[2092],[1889,17102,17104],{"className":17103,"style":8730},[8729],[1889,17105,8483],{"className":17106},[1932],[1889,17108,5733],{"className":17109},[2367],"，方差",[1889,17112,17114,17131],{"className":17113},[1892],[1889,17115,17117],{"className":17116},[1896],[1898,17118,17119],{"xmlns":1900},[1902,17120,17121,17129],{},[1905,17122,17123],{},[2783,17124,17125,17127],{},[1908,17126,8626],{},[1969,17128,1990],{},[1912,17130,10480],{"encoding":1914},[1889,17132,17134],{"className":17133,"ariaHidden":1919},[1918],[1889,17135,17137,17140],{"className":17136},[1923],[1889,17138],{"className":17139,"style":10490},[1927],[1889,17141,17143,17146],{"className":17142},[1932],[1889,17144,8626],{"className":17145,"style":6310},[1932,1933],[1889,17147,17149],{"className":17148},[2071],[1889,17150,17152],{"className":17151},[2075],[1889,17153,17155],{"className":17154},[2080],[1889,17156,17158],{"className":17157,"style":10490},[2084],[1889,17159,17160,17163],{"style":2825},[1889,17161],{"className":17162,"style":2093},[2092],[1889,17164,17166],{"className":17165},[2097,2098,2099,2100],[1889,17167,1990],{"className":17168},[1932,2100],[1808,17170,17171,17172,17241,17242,17270],{},"初始财富",[1889,17173,17175,17192],{"className":17174},[1892],[1889,17176,17178],{"className":17177},[1896],[1898,17179,17180],{"xmlns":1900},[1902,17181,17182,17190],{},[1905,17183,17184],{},[1963,17185,17186,17188],{},[1908,17187,8472],{},[1969,17189,3819],{},[1912,17191,12158],{"encoding":1914},[1889,17193,17195],{"className":17194,"ariaHidden":1919},[1918],[1889,17196,17198,17201],{"className":17197},[1923],[1889,17199],{"className":17200,"style":2475},[1927],[1889,17202,17204,17207],{"className":17203},[1932],[1889,17205,8472],{"className":17206,"style":8687},[1932,1933],[1889,17208,17210],{"className":17209},[2071],[1889,17211,17213,17233],{"className":17212},[2075,2076],[1889,17214,17216,17230],{"className":17215},[2080],[1889,17217,17219],{"className":17218,"style":2085},[2084],[1889,17220,17221,17224],{"style":12188},[1889,17222],{"className":17223,"style":2093},[2092],[1889,17225,17227],{"className":17226},[2097,2098,2099,2100],[1889,17228,3819],{"className":17229},[1932,2100],[1889,17231,2108],{"className":17232},[2107],[1889,17234,17236],{"className":17235},[2080],[1889,17237,17239],{"className":17238,"style":2115},[2084],[1889,17240],{},"，投资",[1889,17243,17245,17258],{"className":17244},[1892],[1889,17246,17248],{"className":17247},[1896],[1898,17249,17250],{"xmlns":1900},[1902,17251,17252,17256],{},[1905,17253,17254],{},[1908,17255,3811],{},[1912,17257,11242],{"encoding":1914},[1889,17259,17261],{"className":17260,"ariaHidden":1919},[1918],[1889,17262,17264,17267],{"className":17263},[1923],[1889,17265],{"className":17266,"style":5332},[1927],[1889,17268,3811],{"className":17269,"style":3842},[1932,1933],"比例于风险资产",[1798,17272,17273,2704],{},[1884,17274,12877],{},[1889,17276,17278],{"className":17277},[1938],[1889,17279,17281,17353],{"className":17280},[1892],[1889,17282,17284],{"className":17283},[1896],[1898,17285,17286],{"xmlns":1900,"display":1947},[1902,17287,17288,17350],{},[1905,17289,17290,17296,17298,17304,17306,17308,17310,17312,17314,17316,17318,17320,17322,17328,17330,17332,17334,17336,17338,17340,17346,17348],{},[8476,17291,17292,17294],{"accent":1919},[1908,17293,8472],{},[1955,17295,8483],{},[1955,17297,1957],{},[1963,17299,17300,17302],{},[1908,17301,8472],{},[1969,17303,3819],{},[1955,17305,5722],{"stretchy":1960},[1955,17307,1961],{"stretchy":1960},[1969,17309,1971],{},[1955,17311,3917],{},[1908,17313,3811],{},[1955,17315,2023],{"stretchy":1960},[1955,17317,1961],{"stretchy":1960},[1969,17319,1971],{},[1955,17321,3910],{},[1963,17323,17324,17326],{},[1908,17325,16887],{},[1908,17327,12241],{},[1955,17329,2023],{"stretchy":1960},[1955,17331,3910],{},[1908,17333,3811],{},[1955,17335,1961],{"stretchy":1960},[1969,17337,1971],{},[1955,17339,3910],{},[8476,17341,17342,17344],{"accent":1919},[1908,17343,16887],{},[1955,17345,8483],{},[1955,17347,2023],{"stretchy":1960},[1955,17349,5733],{"stretchy":1960},[1912,17351,17352],{"encoding":1914},"\\tilde{w} = w_0[(1-\\alpha)(1+r_f) + \\alpha(1+\\tilde{r})]",[1889,17354,17356,17402,17464,17491,17550,17574],{"className":17355,"ariaHidden":1919},[1918],[1889,17357,17359,17362,17393,17396,17399],{"className":17358},[1923],[1889,17360],{"className":17361,"style":8710},[1927],[1889,17363,17365],{"className":17364},[1932,8700],[1889,17366,17368],{"className":17367},[2075],[1889,17369,17371],{"className":17370},[2080],[1889,17372,17374,17382],{"className":17373,"style":8710},[2084],[1889,17375,17376,17379],{"style":8713},[1889,17377],{"className":17378,"style":6746},[2092],[1889,17380,8472],{"className":17381,"style":8687},[1932,1933],[1889,17383,17384,17387],{"style":8722},[1889,17385],{"className":17386,"style":6746},[2092],[1889,17388,17390],{"className":17389,"style":9650},[8729],[1889,17391,8483],{"className":17392},[1932],[1889,17394],{"className":17395,"style":2043},[2042],[1889,17397,1957],{"className":17398},[2047],[1889,17400],{"className":17401,"style":2043},[2042],[1889,17403,17405,17408,17448,17452,17455,17458,17461],{"className":17404},[1923],[1889,17406],{"className":17407,"style":2057},[1927],[1889,17409,17411,17414],{"className":17410},[1932],[1889,17412,8472],{"className":17413,"style":8687},[1932,1933],[1889,17415,17417],{"className":17416},[2071],[1889,17418,17420,17440],{"className":17419},[2075,2076],[1889,17421,17423,17437],{"className":17422},[2080],[1889,17424,17426],{"className":17425,"style":2085},[2084],[1889,17427,17428,17431],{"style":12188},[1889,17429],{"className":17430,"style":2093},[2092],[1889,17432,17434],{"className":17433},[2097,2098,2099,2100],[1889,17435,3819],{"className":17436},[1932,2100],[1889,17438,2108],{"className":17439},[2107],[1889,17441,17443],{"className":17442},[2080],[1889,17444,17446],{"className":17445,"style":2115},[2084],[1889,17447],{},[1889,17449,17451],{"className":17450},[2061],"[(",[1889,17453,1971],{"className":17454},[1932],[1889,17456],{"className":17457,"style":4041},[2042],[1889,17459,3917],{"className":17460},[4045],[1889,17462],{"className":17463,"style":4041},[2042],[1889,17465,17467,17470,17473,17476,17479,17482,17485,17488],{"className":17466},[1923],[1889,17468],{"className":17469,"style":2057},[1927],[1889,17471,3811],{"className":17472,"style":3842},[1932,1933],[1889,17474,2023],{"className":17475},[2367],[1889,17477,1961],{"className":17478},[2061],[1889,17480,1971],{"className":17481},[1932],[1889,17483],{"className":17484,"style":4041},[2042],[1889,17486,3910],{"className":17487},[4045],[1889,17489],{"className":17490,"style":4041},[2042],[1889,17492,17494,17498,17538,17541,17544,17547],{"className":17493},[1923],[1889,17495],{"className":17496,"style":17497},[1927],"height:1.0361em;vertical-align:-0.2861em;",[1889,17499,17501,17504],{"className":17500},[1932],[1889,17502,16887],{"className":17503,"style":16715},[1932,1933],[1889,17505,17507],{"className":17506},[2071],[1889,17508,17510,17530],{"className":17509},[2075,2076],[1889,17511,17513,17527],{"className":17512},[2080],[1889,17514,17516],{"className":17515,"style":16921},[2084],[1889,17517,17518,17521],{"style":16924},[1889,17519],{"className":17520,"style":2093},[2092],[1889,17522,17524],{"className":17523},[2097,2098,2099,2100],[1889,17525,12241],{"className":17526,"style":12322},[1932,1933,2100],[1889,17528,2108],{"className":17529},[2107],[1889,17531,17533],{"className":17532},[2080],[1889,17534,17536],{"className":17535,"style":16943},[2084],[1889,17537],{},[1889,17539,2023],{"className":17540},[2367],[1889,17542],{"className":17543,"style":4041},[2042],[1889,17545,3910],{"className":17546},[4045],[1889,17548],{"className":17549,"style":4041},[2042],[1889,17551,17553,17556,17559,17562,17565,17568,17571],{"className":17552},[1923],[1889,17554],{"className":17555,"style":2057},[1927],[1889,17557,3811],{"className":17558,"style":3842},[1932,1933],[1889,17560,1961],{"className":17561},[2061],[1889,17563,1971],{"className":17564},[1932],[1889,17566],{"className":17567,"style":4041},[2042],[1889,17569,3910],{"className":17570},[4045],[1889,17572],{"className":17573,"style":4041},[2042],[1889,17575,17577,17580,17611],{"className":17576},[1923],[1889,17578],{"className":17579,"style":2057},[1927],[1889,17581,17583],{"className":17582},[1932,8700],[1889,17584,17586],{"className":17585},[2075],[1889,17587,17589],{"className":17588},[2080],[1889,17590,17592,17600],{"className":17591,"style":8710},[2084],[1889,17593,17594,17597],{"style":8713},[1889,17595],{"className":17596,"style":6746},[2092],[1889,17598,16887],{"className":17599,"style":16715},[1932,1933],[1889,17601,17602,17605],{"style":8722},[1889,17603],{"className":17604,"style":6746},[2092],[1889,17606,17608],{"className":17607,"style":8730},[8729],[1889,17609,8483],{"className":17610},[1932],[1889,17612,5972],{"className":17613},[2367],[1889,17615,17617],{"className":17616},[1938],[1889,17618,17620,17682],{"className":17619},[1892],[1889,17621,17623],{"className":17622},[1896],[1898,17624,17625],{"xmlns":1900,"display":1947},[1902,17626,17627,17679],{},[1905,17628,17629,17631,17637,17639,17641,17643,17649,17651,17653,17655,17661,17663,17669,17671,17677],{},[1955,17630,1957],{},[1963,17632,17633,17635],{},[1908,17634,8472],{},[1969,17636,3819],{},[1955,17638,1961],{"stretchy":1960},[1969,17640,1971],{},[1955,17642,3910],{},[1963,17644,17645,17647],{},[1908,17646,16887],{},[1908,17648,12241],{},[1955,17650,2023],{"stretchy":1960},[1955,17652,3910],{},[1908,17654,3811],{},[1963,17656,17657,17659],{},[1908,17658,8472],{},[1969,17660,3819],{},[1955,17662,1961],{"stretchy":1960},[8476,17664,17665,17667],{"accent":1919},[1908,17666,16887],{},[1955,17668,8483],{},[1955,17670,3917],{},[1963,17672,17673,17675],{},[1908,17674,16887],{},[1908,17676,12241],{},[1955,17678,2023],{"stretchy":1960},[1912,17680,17681],{"encoding":1914},"= w_0(1+r_f) + \\alpha w_0(\\tilde{r} - r_f)",[1889,17683,17685,17698,17759,17817,17909],{"className":17684,"ariaHidden":1919},[1918],[1889,17686,17688,17692,17695],{"className":17687},[1923],[1889,17689],{"className":17690,"style":17691},[1927],"height:0.3669em;",[1889,17693,1957],{"className":17694},[2047],[1889,17696],{"className":17697,"style":2043},[2042],[1889,17699,17701,17704,17744,17747,17750,17753,17756],{"className":17700},[1923],[1889,17702],{"className":17703,"style":2057},[1927],[1889,17705,17707,17710],{"className":17706},[1932],[1889,17708,8472],{"className":17709,"style":8687},[1932,1933],[1889,17711,17713],{"className":17712},[2071],[1889,17714,17716,17736],{"className":17715},[2075,2076],[1889,17717,17719,17733],{"className":17718},[2080],[1889,17720,17722],{"className":17721,"style":2085},[2084],[1889,17723,17724,17727],{"style":12188},[1889,17725],{"className":17726,"style":2093},[2092],[1889,17728,17730],{"className":17729},[2097,2098,2099,2100],[1889,17731,3819],{"className":17732},[1932,2100],[1889,17734,2108],{"className":17735},[2107],[1889,17737,17739],{"className":17738},[2080],[1889,17740,17742],{"className":17741,"style":2115},[2084],[1889,17743],{},[1889,17745,1961],{"className":17746},[2061],[1889,17748,1971],{"className":17749},[1932],[1889,17751],{"className":17752,"style":4041},[2042],[1889,17754,3910],{"className":17755},[4045],[1889,17757],{"className":17758,"style":4041},[2042],[1889,17760,17762,17765,17805,17808,17811,17814],{"className":17761},[1923],[1889,17763],{"className":17764,"style":17497},[1927],[1889,17766,17768,17771],{"className":17767},[1932],[1889,17769,16887],{"className":17770,"style":16715},[1932,1933],[1889,17772,17774],{"className":17773},[2071],[1889,17775,17777,17797],{"className":17776},[2075,2076],[1889,17778,17780,17794],{"className":17779},[2080],[1889,17781,17783],{"className":17782,"style":16921},[2084],[1889,17784,17785,17788],{"style":16924},[1889,17786],{"className":17787,"style":2093},[2092],[1889,17789,17791],{"className":17790},[2097,2098,2099,2100],[1889,17792,12241],{"className":17793,"style":12322},[1932,1933,2100],[1889,17795,2108],{"className":17796},[2107],[1889,17798,17800],{"className":17799},[2080],[1889,17801,17803],{"className":17802,"style":16943},[2084],[1889,17804],{},[1889,17806,2023],{"className":17807},[2367],[1889,17809],{"className":17810,"style":4041},[2042],[1889,17812,3910],{"className":17813},[4045],[1889,17815],{"className":17816,"style":4041},[2042],[1889,17818,17820,17823,17826,17866,17869,17900,17903,17906],{"className":17819},[1923],[1889,17821],{"className":17822,"style":2057},[1927],[1889,17824,3811],{"className":17825,"style":3842},[1932,1933],[1889,17827,17829,17832],{"className":17828},[1932],[1889,17830,8472],{"className":17831,"style":8687},[1932,1933],[1889,17833,17835],{"className":17834},[2071],[1889,17836,17838,17858],{"className":17837},[2075,2076],[1889,17839,17841,17855],{"className":17840},[2080],[1889,17842,17844],{"className":17843,"style":2085},[2084],[1889,17845,17846,17849],{"style":12188},[1889,17847],{"className":17848,"style":2093},[2092],[1889,17850,17852],{"className":17851},[2097,2098,2099,2100],[1889,17853,3819],{"className":17854},[1932,2100],[1889,17856,2108],{"className":17857},[2107],[1889,17859,17861],{"className":17860},[2080],[1889,17862,17864],{"className":17863,"style":2115},[2084],[1889,17865],{},[1889,17867,1961],{"className":17868},[2061],[1889,17870,17872],{"className":17871},[1932,8700],[1889,17873,17875],{"className":17874},[2075],[1889,17876,17878],{"className":17877},[2080],[1889,17879,17881,17889],{"className":17880,"style":8710},[2084],[1889,17882,17883,17886],{"style":8713},[1889,17884],{"className":17885,"style":6746},[2092],[1889,17887,16887],{"className":17888,"style":16715},[1932,1933],[1889,17890,17891,17894],{"style":8722},[1889,17892],{"className":17893,"style":6746},[2092],[1889,17895,17897],{"className":17896,"style":8730},[8729],[1889,17898,8483],{"className":17899},[1932],[1889,17901],{"className":17902,"style":4041},[2042],[1889,17904,3917],{"className":17905},[4045],[1889,17907],{"className":17908,"style":4041},[2042],[1889,17910,17912,17915,17955],{"className":17911},[1923],[1889,17913],{"className":17914,"style":17497},[1927],[1889,17916,17918,17921],{"className":17917},[1932],[1889,17919,16887],{"className":17920,"style":16715},[1932,1933],[1889,17922,17924],{"className":17923},[2071],[1889,17925,17927,17947],{"className":17926},[2075,2076],[1889,17928,17930,17944],{"className":17929},[2080],[1889,17931,17933],{"className":17932,"style":16921},[2084],[1889,17934,17935,17938],{"style":16924},[1889,17936],{"className":17937,"style":2093},[2092],[1889,17939,17941],{"className":17940},[2097,2098,2099,2100],[1889,17942,12241],{"className":17943,"style":12322},[1932,1933,2100],[1889,17945,2108],{"className":17946},[2107],[1889,17948,17950],{"className":17949},[2080],[1889,17951,17953],{"className":17952,"style":16943},[2084],[1889,17954],{},[1889,17956,2023],{"className":17957},[2367],[1798,17959,17960,2704],{},[1884,17961,13355],{},[1889,17963,17965],{"className":17964},[1938],[1889,17966,17968,18072],{"className":17967},[1892],[1889,17969,17971],{"className":17970},[1896],[1898,17972,17973],{"xmlns":1900,"display":1947},[1902,17974,17975,18069],{},[1905,17976,17977,17987,17989,17991,17993,17995,17997,18003,18005,18007,18009,18011,18013,18015,18017,18023,18025,18027,18029,18035,18037,18039,18041,18047,18049,18055,18057,18063,18065,18067],{},[13372,17978,17979,17985],{},[1905,17980,17981,17983],{},[1908,17982,13378],{},[1955,17984,7010],{},[1908,17986,3811],{},[2042,17988],{"width":2958},[1908,17990,5719],{"mathvariant":5313},[1955,17992,5722],{"stretchy":1960},[1908,17994,5308],{},[1955,17996,1961],{"stretchy":1960},[8476,17998,17999,18001],{"accent":1919},[1908,18000,8472],{},[1955,18002,8483],{},[1955,18004,2023],{"stretchy":1960},[1955,18006,5733],{"stretchy":1960},[1955,18008,1957],{},[1908,18010,5719],{"mathvariant":5313},[1955,18012,5722],{"stretchy":1960},[1908,18014,5308],{},[1955,18016,1961],{"stretchy":1960},[1963,18018,18019,18021],{},[1908,18020,8472],{},[1969,18022,3819],{},[1955,18024,1961],{"stretchy":1960},[1969,18026,1971],{},[1955,18028,3910],{},[1963,18030,18031,18033],{},[1908,18032,16887],{},[1908,18034,12241],{},[1955,18036,2023],{"stretchy":1960},[1955,18038,3910],{},[1908,18040,3811],{},[1963,18042,18043,18045],{},[1908,18044,8472],{},[1969,18046,3819],{},[1955,18048,1961],{"stretchy":1960},[8476,18050,18051,18053],{"accent":1919},[1908,18052,16887],{},[1955,18054,8483],{},[1955,18056,3917],{},[1963,18058,18059,18061],{},[1908,18060,16887],{},[1908,18062,12241],{},[1955,18064,2023],{"stretchy":1960},[1955,18066,2023],{"stretchy":1960},[1955,18068,5733],{"stretchy":1960},[1912,18070,18071],{"encoding":1914},"\\max_{\\alpha} \\quad \\mathbb{E}[u(\\tilde{w})] = \\mathbb{E}[u(w_0(1+r_f) + \\alpha w_0(\\tilde{r} - r_f))]",[1889,18073,18075,18189,18262,18320,18412],{"className":18074,"ariaHidden":1919},[1918],[1889,18076,18078,18081,18128,18131,18134,18137,18140,18143,18146,18177,18180,18183,18186],{"className":18077},[1923],[1889,18079],{"className":18080,"style":13461},[1927],[1889,18082,18084],{"className":18083},[2571,5778],[1889,18085,18087,18120],{"className":18086},[2075,2076],[1889,18088,18090,18117],{"className":18089},[2080],[1889,18091,18093,18107],{"className":18092,"style":5332},[2084],[1889,18094,18095,18098],{"style":13476},[1889,18096],{"className":18097,"style":6746},[2092],[1889,18099,18101],{"className":18100},[2097,2098,2099,2100],[1889,18102,18104],{"className":18103},[1932,2100],[1889,18105,3811],{"className":18106,"style":3842},[1932,1933,2100],[1889,18108,18109,18112],{"style":8713},[1889,18110],{"className":18111,"style":6746},[2092],[1889,18113,18114],{},[1889,18115,13378],{"className":18116},[2571],[1889,18118,2108],{"className":18119},[2107],[1889,18121,18123],{"className":18122},[2080],[1889,18124,18126],{"className":18125,"style":13505},[2084],[1889,18127],{},[1889,18129],{"className":18130,"style":3061},[2042],[1889,18132],{"className":18133,"style":2125},[2042],[1889,18135,5719],{"className":18136},[1932,5355],[1889,18138,5722],{"className":18139},[2061],[1889,18141,5308],{"className":18142},[1932,1933],[1889,18144,1961],{"className":18145},[2061],[1889,18147,18149],{"className":18148},[1932,8700],[1889,18150,18152],{"className":18151},[2075],[1889,18153,18155],{"className":18154},[2080],[1889,18156,18158,18166],{"className":18157,"style":8710},[2084],[1889,18159,18160,18163],{"style":8713},[1889,18161],{"className":18162,"style":6746},[2092],[1889,18164,8472],{"className":18165,"style":8687},[1932,1933],[1889,18167,18168,18171],{"style":8722},[1889,18169],{"className":18170,"style":6746},[2092],[1889,18172,18174],{"className":18173,"style":9650},[8729],[1889,18175,8483],{"className":18176},[1932],[1889,18178,5972],{"className":18179},[2367],[1889,18181],{"className":18182,"style":2043},[2042],[1889,18184,1957],{"className":18185},[2047],[1889,18187],{"className":18188,"style":2043},[2042],[1889,18190,18192,18195,18198,18201,18204,18207,18247,18250,18253,18256,18259],{"className":18191},[1923],[1889,18193],{"className":18194,"style":2057},[1927],[1889,18196,5719],{"className":18197},[1932,5355],[1889,18199,5722],{"className":18200},[2061],[1889,18202,5308],{"className":18203},[1932,1933],[1889,18205,1961],{"className":18206},[2061],[1889,18208,18210,18213],{"className":18209},[1932],[1889,18211,8472],{"className":18212,"style":8687},[1932,1933],[1889,18214,18216],{"className":18215},[2071],[1889,18217,18219,18239],{"className":18218},[2075,2076],[1889,18220,18222,18236],{"className":18221},[2080],[1889,18223,18225],{"className":18224,"style":2085},[2084],[1889,18226,18227,18230],{"style":12188},[1889,18228],{"className":18229,"style":2093},[2092],[1889,18231,18233],{"className":18232},[2097,2098,2099,2100],[1889,18234,3819],{"className":18235},[1932,2100],[1889,18237,2108],{"className":18238},[2107],[1889,18240,18242],{"className":18241},[2080],[1889,18243,18245],{"className":18244,"style":2115},[2084],[1889,18246],{},[1889,18248,1961],{"className":18249},[2061],[1889,18251,1971],{"className":18252},[1932],[1889,18254],{"className":18255,"style":4041},[2042],[1889,18257,3910],{"className":18258},[4045],[1889,18260],{"className":18261,"style":4041},[2042],[1889,18263,18265,18268,18308,18311,18314,18317],{"className":18264},[1923],[1889,18266],{"className":18267,"style":17497},[1927],[1889,18269,18271,18274],{"className":18270},[1932],[1889,18272,16887],{"className":18273,"style":16715},[1932,1933],[1889,18275,18277],{"className":18276},[2071],[1889,18278,18280,18300],{"className":18279},[2075,2076],[1889,18281,18283,18297],{"className":18282},[2080],[1889,18284,18286],{"className":18285,"style":16921},[2084],[1889,18287,18288,18291],{"style":16924},[1889,18289],{"className":18290,"style":2093},[2092],[1889,18292,18294],{"className":18293},[2097,2098,2099,2100],[1889,18295,12241],{"className":18296,"style":12322},[1932,1933,2100],[1889,18298,2108],{"className":18299},[2107],[1889,18301,18303],{"className":18302},[2080],[1889,18304,18306],{"className":18305,"style":16943},[2084],[1889,18307],{},[1889,18309,2023],{"className":18310},[2367],[1889,18312],{"className":18313,"style":4041},[2042],[1889,18315,3910],{"className":18316},[4045],[1889,18318],{"className":18319,"style":4041},[2042],[1889,18321,18323,18326,18329,18369,18372,18403,18406,18409],{"className":18322},[1923],[1889,18324],{"className":18325,"style":2057},[1927],[1889,18327,3811],{"className":18328,"style":3842},[1932,1933],[1889,18330,18332,18335],{"className":18331},[1932],[1889,18333,8472],{"className":18334,"style":8687},[1932,1933],[1889,18336,18338],{"className":18337},[2071],[1889,18339,18341,18361],{"className":18340},[2075,2076],[1889,18342,18344,18358],{"className":18343},[2080],[1889,18345,18347],{"className":18346,"style":2085},[2084],[1889,18348,18349,18352],{"style":12188},[1889,18350],{"className":18351,"style":2093},[2092],[1889,18353,18355],{"className":18354},[2097,2098,2099,2100],[1889,18356,3819],{"className":18357},[1932,2100],[1889,18359,2108],{"className":18360},[2107],[1889,18362,18364],{"className":18363},[2080],[1889,18365,18367],{"className":18366,"style":2115},[2084],[1889,18368],{},[1889,18370,1961],{"className":18371},[2061],[1889,18373,18375],{"className":18374},[1932,8700],[1889,18376,18378],{"className":18377},[2075],[1889,18379,18381],{"className":18380},[2080],[1889,18382,18384,18392],{"className":18383,"style":8710},[2084],[1889,18385,18386,18389],{"style":8713},[1889,18387],{"className":18388,"style":6746},[2092],[1889,18390,16887],{"className":18391,"style":16715},[1932,1933],[1889,18393,18394,18397],{"style":8722},[1889,18395],{"className":18396,"style":6746},[2092],[1889,18398,18400],{"className":18399,"style":8730},[8729],[1889,18401,8483],{"className":18402},[1932],[1889,18404],{"className":18405,"style":4041},[2042],[1889,18407,3917],{"className":18408},[4045],[1889,18410],{"className":18411,"style":4041},[2042],[1889,18413,18415,18418,18458],{"className":18414},[1923],[1889,18416],{"className":18417,"style":17497},[1927],[1889,18419,18421,18424],{"className":18420},[1932],[1889,18422,16887],{"className":18423,"style":16715},[1932,1933],[1889,18425,18427],{"className":18426},[2071],[1889,18428,18430,18450],{"className":18429},[2075,2076],[1889,18431,18433,18447],{"className":18432},[2080],[1889,18434,18436],{"className":18435,"style":16921},[2084],[1889,18437,18438,18441],{"style":16924},[1889,18439],{"className":18440,"style":2093},[2092],[1889,18442,18444],{"className":18443},[2097,2098,2099,2100],[1889,18445,12241],{"className":18446,"style":12322},[1932,1933,2100],[1889,18448,2108],{"className":18449},[2107],[1889,18451,18453],{"className":18452},[2080],[1889,18454,18456],{"className":18455,"style":16943},[2084],[1889,18457],{},[1889,18459,18461],{"className":18460},[2367],"))]",[1877,18463,18465],{"id":18464},"_42-最优投资比例","4.2 最优投资比例",[1798,18467,18468,2704],{},[1884,18469,13819],{},[1889,18471,18473],{"className":18472},[1938],[1889,18474,18476,18540],{"className":18475},[1892],[1889,18477,18479],{"className":18478},[1896],[1898,18480,18481],{"xmlns":1900,"display":1947},[1902,18482,18483,18537],{},[1905,18484,18485,18487,18489,18495,18497,18503,18505,18507,18513,18515,18521,18523,18529,18531,18533,18535],{},[1908,18486,5719],{"mathvariant":5313},[1955,18488,5722],{"stretchy":1960},[2783,18490,18491,18493],{},[1908,18492,5308],{},[1955,18494,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,18496,1961],{"stretchy":1960},[8476,18498,18499,18501],{"accent":1919},[1908,18500,8472],{},[1955,18502,8483],{},[1955,18504,2023],{"stretchy":1960},[1955,18506,6212],{},[1963,18508,18509,18511],{},[1908,18510,8472],{},[1969,18512,3819],{},[1955,18514,1961],{"stretchy":1960},[8476,18516,18517,18519],{"accent":1919},[1908,18518,16887],{},[1955,18520,8483],{},[1955,18522,3917],{},[1963,18524,18525,18527],{},[1908,18526,16887],{},[1908,18528,12241],{},[1955,18530,2023],{"stretchy":1960},[1955,18532,5733],{"stretchy":1960},[1955,18534,1957],{},[1969,18536,3819],{},[1912,18538,18539],{"encoding":1914},"\\mathbb{E}[u'(\\tilde{w}) \\cdot w_0(\\tilde{r} - r_f)] = 0",[1889,18541,18543,18634,18723,18781],{"className":18542,"ariaHidden":1919},[1918],[1889,18544,18546,18550,18553,18556,18588,18591,18622,18625,18628,18631],{"className":18545},[1923],[1889,18547],{"className":18548,"style":18549},[1927],"height:1.0519em;vertical-align:-0.25em;",[1889,18551,5719],{"className":18552},[1932,5355],[1889,18554,5722],{"className":18555},[2061],[1889,18557,18559,18562],{"className":18558},[1932],[1889,18560,5308],{"className":18561},[1932,1933],[1889,18563,18565],{"className":18564},[2071],[1889,18566,18568],{"className":18567},[2075],[1889,18569,18571],{"className":18570},[2080],[1889,18572,18574],{"className":18573,"style":3042},[2084],[1889,18575,18576,18579],{"style":3045},[1889,18577],{"className":18578,"style":2093},[2092],[1889,18580,18582],{"className":18581},[2097,2098,2099,2100],[1889,18583,18585],{"className":18584},[1932,2100],[1889,18586,2791],{"className":18587},[1932,2100],[1889,18589,1961],{"className":18590},[2061],[1889,18592,18594],{"className":18593},[1932,8700],[1889,18595,18597],{"className":18596},[2075],[1889,18598,18600],{"className":18599},[2080],[1889,18601,18603,18611],{"className":18602,"style":8710},[2084],[1889,18604,18605,18608],{"style":8713},[1889,18606],{"className":18607,"style":6746},[2092],[1889,18609,8472],{"className":18610,"style":8687},[1932,1933],[1889,18612,18613,18616],{"style":8722},[1889,18614],{"className":18615,"style":6746},[2092],[1889,18617,18619],{"className":18618,"style":9650},[8729],[1889,18620,8483],{"className":18621},[1932],[1889,18623,2023],{"className":18624},[2367],[1889,18626],{"className":18627,"style":4041},[2042],[1889,18629,6212],{"className":18630},[4045],[1889,18632],{"className":18633,"style":4041},[2042],[1889,18635,18637,18640,18680,18683,18714,18717,18720],{"className":18636},[1923],[1889,18638],{"className":18639,"style":2057},[1927],[1889,18641,18643,18646],{"className":18642},[1932],[1889,18644,8472],{"className":18645,"style":8687},[1932,1933],[1889,18647,18649],{"className":18648},[2071],[1889,18650,18652,18672],{"className":18651},[2075,2076],[1889,18653,18655,18669],{"className":18654},[2080],[1889,18656,18658],{"className":18657,"style":2085},[2084],[1889,18659,18660,18663],{"style":12188},[1889,18661],{"className":18662,"style":2093},[2092],[1889,18664,18666],{"className":18665},[2097,2098,2099,2100],[1889,18667,3819],{"className":18668},[1932,2100],[1889,18670,2108],{"className":18671},[2107],[1889,18673,18675],{"className":18674},[2080],[1889,18676,18678],{"className":18677,"style":2115},[2084],[1889,18679],{},[1889,18681,1961],{"className":18682},[2061],[1889,18684,18686],{"className":18685},[1932,8700],[1889,18687,18689],{"className":18688},[2075],[1889,18690,18692],{"className":18691},[2080],[1889,18693,18695,18703],{"className":18694,"style":8710},[2084],[1889,18696,18697,18700],{"style":8713},[1889,18698],{"className":18699,"style":6746},[2092],[1889,18701,16887],{"className":18702,"style":16715},[1932,1933],[1889,18704,18705,18708],{"style":8722},[1889,18706],{"className":18707,"style":6746},[2092],[1889,18709,18711],{"className":18710,"style":8730},[8729],[1889,18712,8483],{"className":18713},[1932],[1889,18715],{"className":18716,"style":4041},[2042],[1889,18718,3917],{"className":18719},[4045],[1889,18721],{"className":18722,"style":4041},[2042],[1889,18724,18726,18729,18769,18772,18775,18778],{"className":18725},[1923],[1889,18727],{"className":18728,"style":17497},[1927],[1889,18730,18732,18735],{"className":18731},[1932],[1889,18733,16887],{"className":18734,"style":16715},[1932,1933],[1889,18736,18738],{"className":18737},[2071],[1889,18739,18741,18761],{"className":18740},[2075,2076],[1889,18742,18744,18758],{"className":18743},[2080],[1889,18745,18747],{"className":18746,"style":16921},[2084],[1889,18748,18749,18752],{"style":16924},[1889,18750],{"className":18751,"style":2093},[2092],[1889,18753,18755],{"className":18754},[2097,2098,2099,2100],[1889,18756,12241],{"className":18757,"style":12322},[1932,1933,2100],[1889,18759,2108],{"className":18760},[2107],[1889,18762,18764],{"className":18763},[2080],[1889,18765,18767],{"className":18766,"style":16943},[2084],[1889,18768],{},[1889,18770,5972],{"className":18771},[2367],[1889,18773],{"className":18774,"style":2043},[2042],[1889,18776,1957],{"className":18777},[2047],[1889,18779],{"className":18780,"style":2043},[2042],[1889,18782,18784,18787],{"className":18783},[1923],[1889,18785],{"className":18786,"style":2694},[1927],[1889,18788,3819],{"className":18789},[1932],[1798,18791,18792,2704],{},[1884,18793,18794],{},"展开",[1889,18796,18798],{"className":18797},[1938],[1889,18799,18801,18857],{"className":18800},[1892],[1889,18802,18804],{"className":18803},[1896],[1898,18805,18806],{"xmlns":1900,"display":1947},[1902,18807,18808,18854],{},[1905,18809,18810,18812,18814,18820,18822,18828,18830,18832,18838,18840,18846,18848,18850,18852],{},[1908,18811,5719],{"mathvariant":5313},[1955,18813,5722],{"stretchy":1960},[2783,18815,18816,18818],{},[1908,18817,5308],{},[1955,18819,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,18821,1961],{"stretchy":1960},[8476,18823,18824,18826],{"accent":1919},[1908,18825,8472],{},[1955,18827,8483],{},[1955,18829,2023],{"stretchy":1960},[1955,18831,1961],{"stretchy":1960},[8476,18833,18834,18836],{"accent":1919},[1908,18835,16887],{},[1955,18837,8483],{},[1955,18839,3917],{},[1963,18841,18842,18844],{},[1908,18843,16887],{},[1908,18845,12241],{},[1955,18847,2023],{"stretchy":1960},[1955,18849,5733],{"stretchy":1960},[1955,18851,1957],{},[1969,18853,3819],{},[1912,18855,18856],{"encoding":1914},"\\mathbb{E}[u'(\\tilde{w})(\\tilde{r} - r_f)] = 0",[1889,18858,18860,18984,19042],{"className":18859,"ariaHidden":1919},[1918],[1889,18861,18863,18866,18869,18872,18904,18907,18938,18941,18944,18975,18978,18981],{"className":18862},[1923],[1889,18864],{"className":18865,"style":18549},[1927],[1889,18867,5719],{"className":18868},[1932,5355],[1889,18870,5722],{"className":18871},[2061],[1889,18873,18875,18878],{"className":18874},[1932],[1889,18876,5308],{"className":18877},[1932,1933],[1889,18879,18881],{"className":18880},[2071],[1889,18882,18884],{"className":18883},[2075],[1889,18885,18887],{"className":18886},[2080],[1889,18888,18890],{"className":18889,"style":3042},[2084],[1889,18891,18892,18895],{"style":3045},[1889,18893],{"className":18894,"style":2093},[2092],[1889,18896,18898],{"className":18897},[2097,2098,2099,2100],[1889,18899,18901],{"className":18900},[1932,2100],[1889,18902,2791],{"className":18903},[1932,2100],[1889,18905,1961],{"className":18906},[2061],[1889,18908,18910],{"className":18909},[1932,8700],[1889,18911,18913],{"className":18912},[2075],[1889,18914,18916],{"className":18915},[2080],[1889,18917,18919,18927],{"className":18918,"style":8710},[2084],[1889,18920,18921,18924],{"style":8713},[1889,18922],{"className":18923,"style":6746},[2092],[1889,18925,8472],{"className":18926,"style":8687},[1932,1933],[1889,18928,18929,18932],{"style":8722},[1889,18930],{"className":18931,"style":6746},[2092],[1889,18933,18935],{"className":18934,"style":9650},[8729],[1889,18936,8483],{"className":18937},[1932],[1889,18939,2023],{"className":18940},[2367],[1889,18942,1961],{"className":18943},[2061],[1889,18945,18947],{"className":18946},[1932,8700],[1889,18948,18950],{"className":18949},[2075],[1889,18951,18953],{"className":18952},[2080],[1889,18954,18956,18964],{"className":18955,"style":8710},[2084],[1889,18957,18958,18961],{"style":8713},[1889,18959],{"className":18960,"style":6746},[2092],[1889,18962,16887],{"className":18963,"style":16715},[1932,1933],[1889,18965,18966,18969],{"style":8722},[1889,18967],{"className":18968,"style":6746},[2092],[1889,18970,18972],{"className":18971,"style":8730},[8729],[1889,18973,8483],{"className":18974},[1932],[1889,18976],{"className":18977,"style":4041},[2042],[1889,18979,3917],{"className":18980},[4045],[1889,18982],{"className":18983,"style":4041},[2042],[1889,18985,18987,18990,19030,19033,19036,19039],{"className":18986},[1923],[1889,18988],{"className":18989,"style":17497},[1927],[1889,18991,18993,18996],{"className":18992},[1932],[1889,18994,16887],{"className":18995,"style":16715},[1932,1933],[1889,18997,18999],{"className":18998},[2071],[1889,19000,19002,19022],{"className":19001},[2075,2076],[1889,19003,19005,19019],{"className":19004},[2080],[1889,19006,19008],{"className":19007,"style":16921},[2084],[1889,19009,19010,19013],{"style":16924},[1889,19011],{"className":19012,"style":2093},[2092],[1889,19014,19016],{"className":19015},[2097,2098,2099,2100],[1889,19017,12241],{"className":19018,"style":12322},[1932,1933,2100],[1889,19020,2108],{"className":19021},[2107],[1889,19023,19025],{"className":19024},[2080],[1889,19026,19028],{"className":19027,"style":16943},[2084],[1889,19029],{},[1889,19031,5972],{"className":19032},[2367],[1889,19034],{"className":19035,"style":2043},[2042],[1889,19037,1957],{"className":19038},[2047],[1889,19040],{"className":19041,"style":2043},[2042],[1889,19043,19045,19048],{"className":19044},[1923],[1889,19046],{"className":19047,"style":2694},[1927],[1889,19049,3819],{"className":19050},[1932],[1798,19052,19053],{},"这个条件在一般情况下难以求解，但可以得到定性结果。",[1798,19055,19056,4127,19058,19151,19152,19255],{},[1884,19057,15716],{},[1889,19059,19061,19083],{"className":19060},[1892],[1889,19062,19064],{"className":19063},[1896],[1898,19065,19066],{"xmlns":1900},[1902,19067,19068,19080],{},[1905,19069,19070,19072,19074],{},[1908,19071,17025],{},[1955,19073,6369],{},[1963,19075,19076,19078],{},[1908,19077,16887],{},[1908,19079,12241],{},[1912,19081,19082],{"encoding":1914},"\\mu > r_f",[1889,19084,19086,19105],{"className":19085,"ariaHidden":1919},[1918],[1889,19087,19089,19093,19096,19099,19102],{"className":19088},[1923],[1889,19090],{"className":19091,"style":19092},[1927],"height:0.7335em;vertical-align:-0.1944em;",[1889,19094,17025],{"className":19095},[1932,1933],[1889,19097],{"className":19098,"style":2043},[2042],[1889,19100,6369],{"className":19101},[2047],[1889,19103],{"className":19104,"style":2043},[2042],[1889,19106,19108,19111],{"className":19107},[1923],[1889,19109],{"className":19110,"style":16902},[1927],[1889,19112,19114,19117],{"className":19113},[1932],[1889,19115,16887],{"className":19116,"style":16715},[1932,1933],[1889,19118,19120],{"className":19119},[2071],[1889,19121,19123,19143],{"className":19122},[2075,2076],[1889,19124,19126,19140],{"className":19125},[2080],[1889,19127,19129],{"className":19128,"style":16921},[2084],[1889,19130,19131,19134],{"style":16924},[1889,19132],{"className":19133,"style":2093},[2092],[1889,19135,19137],{"className":19136},[2097,2098,2099,2100],[1889,19138,12241],{"className":19139,"style":12322},[1932,1933,2100],[1889,19141,2108],{"className":19142},[2107],[1889,19144,19146],{"className":19145},[2080],[1889,19147,19149],{"className":19148,"style":16943},[2084],[1889,19150],{},"（风险溢价为正）且投资者风险规避，则",[1889,19153,19155,19181],{"className":19154},[1892],[1889,19156,19158],{"className":19157},[1896],[1898,19159,19160],{"xmlns":1900},[1902,19161,19162,19178],{},[1905,19163,19164,19166,19168,19174,19176],{},[1969,19165,3819],{},[1955,19167,8012],{},[2783,19169,19170,19172],{},[1908,19171,3811],{},[1955,19173,15587],{},[1955,19175,8012],{},[1969,19177,1971],{},[1912,19179,19180],{"encoding":1914},"0 \u003C \\alpha^* \u003C 1",[1889,19182,19184,19202,19246],{"className":19183,"ariaHidden":1919},[1918],[1889,19185,19187,19190,19193,19196,19199],{"className":19186},[1923],[1889,19188],{"className":19189,"style":16786},[1927],[1889,19191,3819],{"className":19192},[1932],[1889,19194],{"className":19195,"style":2043},[2042],[1889,19197,8012],{"className":19198},[2047],[1889,19200],{"className":19201,"style":2043},[2042],[1889,19203,19205,19208,19237,19240,19243],{"className":19204},[1923],[1889,19206],{"className":19207,"style":15806},[1927],[1889,19209,19211,19214],{"className":19210},[1932],[1889,19212,3811],{"className":19213,"style":3842},[1932,1933],[1889,19215,19217],{"className":19216},[2071],[1889,19218,19220],{"className":19219},[2075],[1889,19221,19223],{"className":19222},[2080],[1889,19224,19226],{"className":19225,"style":15604},[2084],[1889,19227,19228,19231],{"style":2825},[1889,19229],{"className":19230,"style":2093},[2092],[1889,19232,19234],{"className":19233},[2097,2098,2099,2100],[1889,19235,15587],{"className":19236},[4045,2100],[1889,19238],{"className":19239,"style":2043},[2042],[1889,19241,8012],{"className":19242},[2047],[1889,19244],{"className":19245,"style":2043},[2042],[1889,19247,19249,19252],{"className":19248},[1923],[1889,19250],{"className":19251,"style":2694},[1927],[1889,19253,1971],{"className":19254},[1932],"（持有正比例的风险资产，但不全部投资）。",[1877,19257,19259],{"id":19258},"_43-cara效用下的明确解","4.3 CARA效用下的明确解",[1798,19261,19262,19263,19379,19380,2698],{},"假设",[1889,19264,19266,19302],{"className":19265},[1892],[1889,19267,19269],{"className":19268},[1896],[1898,19270,19271],{"xmlns":1900},[1902,19272,19273,19299],{},[1905,19274,19275,19277,19279,19281,19283,19285,19287],{},[1908,19276,5308],{},[1955,19278,1961],{"stretchy":1960},[1908,19280,8472],{},[1955,19282,2023],{"stretchy":1960},[1955,19284,1957],{},[1955,19286,3917],{},[2783,19288,19289,19291],{},[1908,19290,11160],{},[1905,19292,19293,19295,19297],{},[1955,19294,3917],{},[1908,19296,3811],{},[1908,19298,8472],{},[1912,19300,19301],{"encoding":1914},"u(w) = -e^{-\\alpha w}",[1889,19303,19305,19332],{"className":19304,"ariaHidden":1919},[1918],[1889,19306,19308,19311,19314,19317,19320,19323,19326,19329],{"className":19307},[1923],[1889,19309],{"className":19310,"style":2057},[1927],[1889,19312,5308],{"className":19313},[1932,1933],[1889,19315,1961],{"className":19316},[2061],[1889,19318,8472],{"className":19319,"style":8687},[1932,1933],[1889,19321,2023],{"className":19322},[2367],[1889,19324],{"className":19325,"style":2043},[2042],[1889,19327,1957],{"className":19328},[2047],[1889,19330],{"className":19331,"style":2043},[2042],[1889,19333,19335,19338,19341],{"className":19334},[1923],[1889,19336],{"className":19337,"style":11181},[1927],[1889,19339,3917],{"className":19340},[1932],[1889,19342,19344,19347],{"className":19343},[1932],[1889,19345,11160],{"className":19346},[1932,1933],[1889,19348,19350],{"className":19349},[2071],[1889,19351,19353],{"className":19352},[2075],[1889,19354,19356],{"className":19355},[2080],[1889,19357,19359],{"className":19358,"style":11203},[2084],[1889,19360,19361,19364],{"style":2825},[1889,19362],{"className":19363,"style":2093},[2092],[1889,19365,19367],{"className":19366},[2097,2098,2099,2100],[1889,19368,19370,19373,19376],{"className":19369},[1932,2100],[1889,19371,3917],{"className":19372},[1932,2100],[1889,19374,3811],{"className":19375,"style":3842},[1932,1933,2100],[1889,19377,8472],{"className":19378,"style":8687},[1932,1933,2100],"（CARA），且",[1889,19381,19383,19420],{"className":19382},[1892],[1889,19384,19386],{"className":19385},[1896],[1898,19387,19388],{"xmlns":1900},[1902,19389,19390,19417],{},[1905,19391,19392,19398,19400,19403,19405,19407,19409,19415],{},[8476,19393,19394,19396],{"accent":1919},[1908,19395,16887],{},[1955,19397,8483],{},[1955,19399,2985],{},[1908,19401,19402],{},"N",[1955,19404,1961],{"stretchy":1960},[1908,19406,17025],{},[1955,19408,1974],{"separator":1919},[2783,19410,19411,19413],{},[1908,19412,8626],{},[1969,19414,1990],{},[1955,19416,2023],{"stretchy":1960},[1912,19418,19419],{"encoding":1914},"\\tilde{r} \\sim N(\\mu, \\sigma^2)",[1889,19421,19423,19469],{"className":19422,"ariaHidden":1919},[1918],[1889,19424,19426,19429,19460,19463,19466],{"className":19425},[1923],[1889,19427],{"className":19428,"style":8710},[1927],[1889,19430,19432],{"className":19431},[1932,8700],[1889,19433,19435],{"className":19434},[2075],[1889,19436,19438],{"className":19437},[2080],[1889,19439,19441,19449],{"className":19440,"style":8710},[2084],[1889,19442,19443,19446],{"style":8713},[1889,19444],{"className":19445,"style":6746},[2092],[1889,19447,16887],{"className":19448,"style":16715},[1932,1933],[1889,19450,19451,19454],{"style":8722},[1889,19452],{"className":19453,"style":6746},[2092],[1889,19455,19457],{"className":19456,"style":8730},[8729],[1889,19458,8483],{"className":19459},[1932],[1889,19461],{"className":19462,"style":2043},[2042],[1889,19464,2985],{"className":19465},[2047],[1889,19467],{"className":19468,"style":2043},[2042],[1889,19470,19472,19476,19479,19482,19485,19488,19491,19520],{"className":19471},[1923],[1889,19473],{"className":19474,"style":19475},[1927],"height:1.0641em;vertical-align:-0.25em;",[1889,19477,19402],{"className":19478,"style":5749},[1932,1933],[1889,19480,1961],{"className":19481},[2061],[1889,19483,17025],{"className":19484},[1932,1933],[1889,19486,1974],{"className":19487},[2121],[1889,19489],{"className":19490,"style":2125},[2042],[1889,19492,19494,19497],{"className":19493},[1932],[1889,19495,8626],{"className":19496,"style":6310},[1932,1933],[1889,19498,19500],{"className":19499},[2071],[1889,19501,19503],{"className":19502},[2075],[1889,19504,19506],{"className":19505},[2080],[1889,19507,19509],{"className":19508,"style":10490},[2084],[1889,19510,19511,19514],{"style":2825},[1889,19512],{"className":19513,"style":2093},[2092],[1889,19515,19517],{"className":19516},[2097,2098,2099,2100],[1889,19518,1990],{"className":19519},[1932,2100],[1889,19521,2023],{"className":19522},[2367],[1798,19524,19525],{},"利用正态分布下期望效用的性质：",[1889,19527,19529],{"className":19528},[1938],[1889,19530,19532,19618],{"className":19531},[1892],[1889,19533,19535],{"className":19534},[1896],[1898,19536,19537],{"xmlns":1900,"display":1947},[1902,19538,19539,19615],{},[1905,19540,19541,19543,19545,19547,19549,19555,19557,19559,19561,19563,19566,19568],{},[1908,19542,5719],{"mathvariant":5313},[1955,19544,5722],{"stretchy":1960},[1908,19546,5308],{},[1955,19548,1961],{"stretchy":1960},[8476,19550,19551,19553],{"accent":1919},[1908,19552,8472],{},[1955,19554,8483],{},[1955,19556,2023],{"stretchy":1960},[1955,19558,5733],{"stretchy":1960},[1955,19560,1957],{},[1955,19562,3917],{},[1908,19564,19565],{},"exp",[1955,19567,7010],{},[1905,19569,19570,19572,19574,19576,19578,19580,19586,19588,19590,19600,19603,19605,19611,19613],{},[1955,19571,1961],{"fence":1919},[1955,19573,3917],{},[1908,19575,3811],{},[1908,19577,5719],{"mathvariant":5313},[1955,19579,5722],{"stretchy":1960},[8476,19581,19582,19584],{"accent":1919},[1908,19583,8472],{},[1955,19585,8483],{},[1955,19587,5733],{"stretchy":1960},[1955,19589,3910],{},[6567,19591,19592,19598],{},[2783,19593,19594,19596],{},[1908,19595,3811],{},[1969,19597,1990],{},[1969,19599,1990],{},[2960,19601,19602],{},"Var",[1955,19604,1961],{"stretchy":1960},[8476,19606,19607,19609],{"accent":1919},[1908,19608,8472],{},[1955,19610,8483],{},[1955,19612,2023],{"stretchy":1960},[1955,19614,2023],{"fence":1919},[1912,19616,19617],{"encoding":1914},"\\mathbb{E}[u(\\tilde{w})] = -\\exp\\left(-\\alpha \\mathbb{E}[\\tilde{w}] + \\frac{\\alpha^2}{2}\\text{Var}(\\tilde{w})\\right)",[1889,19619,19621,19682],{"className":19620,"ariaHidden":1919},[1918],[1889,19622,19624,19627,19630,19633,19636,19639,19670,19673,19676,19679],{"className":19623},[1923],[1889,19625],{"className":19626,"style":2057},[1927],[1889,19628,5719],{"className":19629},[1932,5355],[1889,19631,5722],{"className":19632},[2061],[1889,19634,5308],{"className":19635},[1932,1933],[1889,19637,1961],{"className":19638},[2061],[1889,19640,19642],{"className":19641},[1932,8700],[1889,19643,19645],{"className":19644},[2075],[1889,19646,19648],{"className":19647},[2080],[1889,19649,19651,19659],{"className":19650,"style":8710},[2084],[1889,19652,19653,19656],{"style":8713},[1889,19654],{"className":19655,"style":6746},[2092],[1889,19657,8472],{"className":19658,"style":8687},[1932,1933],[1889,19660,19661,19664],{"style":8722},[1889,19662],{"className":19663,"style":6746},[2092],[1889,19665,19667],{"className":19666,"style":9650},[8729],[1889,19668,8483],{"className":19669},[1932],[1889,19671,5972],{"className":19672},[2367],[1889,19674],{"className":19675,"style":2043},[2042],[1889,19677,1957],{"className":19678},[2047],[1889,19680],{"className":19681,"style":2043},[2042],[1889,19683,19685,19689,19692,19695,19698,19701],{"className":19684},[1923],[1889,19686],{"className":19687,"style":19688},[1927],"height:2.4411em;vertical-align:-0.95em;",[1889,19690,3917],{"className":19691},[1932],[1889,19693],{"className":19694,"style":2125},[2042],[1889,19696,19565],{"className":19697},[2571],[1889,19699],{"className":19700,"style":2125},[2042],[1889,19702,19704,19713,19716,19719,19722,19725,19756,19759,19762,19765,19768,19857,19863,19866,19897,19900],{"className":19703},[2267],[1889,19705,19709],{"className":19706,"style":19708},[2061,19707],"delimcenter","top:0em;",[1889,19710,1961],{"className":19711},[19712,2099],"delimsizing",[1889,19714,3917],{"className":19715},[1932],[1889,19717,3811],{"className":19718,"style":3842},[1932,1933],[1889,19720,5719],{"className":19721},[1932,5355],[1889,19723,5722],{"className":19724},[2061],[1889,19726,19728],{"className":19727},[1932,8700],[1889,19729,19731],{"className":19730},[2075],[1889,19732,19734],{"className":19733},[2080],[1889,19735,19737,19745],{"className":19736,"style":8710},[2084],[1889,19738,19739,19742],{"style":8713},[1889,19740],{"className":19741,"style":6746},[2092],[1889,19743,8472],{"className":19744,"style":8687},[1932,1933],[1889,19746,19747,19750],{"style":8722},[1889,19748],{"className":19749,"style":6746},[2092],[1889,19751,19753],{"className":19752,"style":9650},[8729],[1889,19754,8483],{"className":19755},[1932],[1889,19757,5733],{"className":19758},[2367],[1889,19760],{"className":19761,"style":4041},[2042],[1889,19763,3910],{"className":19764},[4045],[1889,19766],{"className":19767,"style":4041},[2042],[1889,19769,19771,19774,19854],{"className":19770},[1932],[1889,19772],{"className":19773},[2061,6726],[1889,19775,19777],{"className":19776},[6567],[1889,19778,19780,19846],{"className":19779},[2075,2076],[1889,19781,19783,19843],{"className":19782},[2080],[1889,19784,19787,19798,19806],{"className":19785,"style":19786},[2084],"height:1.4911em;",[1889,19788,19789,19792],{"style":6742},[1889,19790],{"className":19791,"style":6746},[2092],[1889,19793,19795],{"className":19794},[1932],[1889,19796,1990],{"className":19797},[1932],[1889,19799,19800,19803],{"style":6783},[1889,19801],{"className":19802,"style":6746},[2092],[1889,19804],{"className":19805,"style":6791},[6790],[1889,19807,19808,19811],{"style":6794},[1889,19809],{"className":19810,"style":6746},[2092],[1889,19812,19814],{"className":19813},[1932],[1889,19815,19817,19820],{"className":19816},[1932],[1889,19818,3811],{"className":19819,"style":3842},[1932,1933],[1889,19821,19823],{"className":19822},[2071],[1889,19824,19826],{"className":19825},[2075],[1889,19827,19829],{"className":19828},[2080],[1889,19830,19832],{"className":19831,"style":10490},[2084],[1889,19833,19834,19837],{"style":2825},[1889,19835],{"className":19836,"style":2093},[2092],[1889,19838,19840],{"className":19839},[2097,2098,2099,2100],[1889,19841,1990],{"className":19842},[1932,2100],[1889,19844,2108],{"className":19845},[2107],[1889,19847,19849],{"className":19848},[2080],[1889,19850,19852],{"className":19851,"style":6813},[2084],[1889,19853],{},[1889,19855],{"className":19856},[2367,6726],[1889,19858,19860],{"className":19859},[1932,3065],[1889,19861,19602],{"className":19862},[1932],[1889,19864,1961],{"className":19865},[2061],[1889,19867,19869],{"className":19868},[1932,8700],[1889,19870,19872],{"className":19871},[2075],[1889,19873,19875],{"className":19874},[2080],[1889,19876,19878,19886],{"className":19877,"style":8710},[2084],[1889,19879,19880,19883],{"style":8713},[1889,19881],{"className":19882,"style":6746},[2092],[1889,19884,8472],{"className":19885,"style":8687},[1932,1933],[1889,19887,19888,19891],{"style":8722},[1889,19889],{"className":19890,"style":6746},[2092],[1889,19892,19894],{"className":19893,"style":9650},[8729],[1889,19895,8483],{"className":19896},[1932],[1889,19898,2023],{"className":19899},[2367],[1889,19901,19903],{"className":19902,"style":19708},[2367,19707],[1889,19904,2023],{"className":19905},[19712,2099],[1798,19907,19908],{},"其中：",[1889,19910,19912],{"className":19911},[1938],[1889,19913,19915,20051],{"className":19914},[1892],[1889,19916,19918],{"className":19917},[1896],[1898,19919,19920],{"xmlns":1900,"display":1947},[1902,19921,19922,20048],{},[8447,19923,19924,19998],{"rowspacing":8449,"columnalign":8450,"columnspacing":2790},[8452,19925,19926,19944],{},[8455,19927,19928],{},[8458,19929,19930],{"scriptlevel":3819,"displaystyle":1919},[1905,19931,19932,19934,19936,19942],{},[1908,19933,5719],{"mathvariant":5313},[1955,19935,5722],{"stretchy":1960},[8476,19937,19938,19940],{"accent":1919},[1908,19939,8472],{},[1955,19941,8483],{},[1955,19943,5733],{"stretchy":1960},[8455,19945,19946],{},[8458,19947,19948],{"scriptlevel":3819,"displaystyle":1919},[1905,19949,19950,19952,19954,19960,19962,19964,19966,19972,19974,19976,19978,19984,19986,19988,19990,19996],{},[1905,19951],{},[1955,19953,1957],{},[1963,19955,19956,19958],{},[1908,19957,8472],{},[1969,19959,3819],{},[1955,19961,1961],{"stretchy":1960},[1969,19963,1971],{},[1955,19965,3910],{},[1963,19967,19968,19970],{},[1908,19969,16887],{},[1908,19971,12241],{},[1955,19973,2023],{"stretchy":1960},[1955,19975,3910],{},[1908,19977,3811],{},[1963,19979,19980,19982],{},[1908,19981,8472],{},[1969,19983,3819],{},[1955,19985,1961],{"stretchy":1960},[1908,19987,17025],{},[1955,19989,3917],{},[1963,19991,19992,19994],{},[1908,19993,16887],{},[1908,19995,12241],{},[1955,19997,2023],{"stretchy":1960},[8452,19999,20000,20018],{},[8455,20001,20002],{},[8458,20003,20004],{"scriptlevel":3819,"displaystyle":1919},[1905,20005,20006,20008,20010,20016],{},[2960,20007,19602],{},[1955,20009,1961],{"stretchy":1960},[8476,20011,20012,20014],{"accent":1919},[1908,20013,8472],{},[1955,20015,8483],{},[1955,20017,2023],{"stretchy":1960},[8455,20019,20020],{},[8458,20021,20022],{"scriptlevel":3819,"displaystyle":1919},[1905,20023,20024,20026,20028,20034,20042],{},[1905,20025],{},[1955,20027,1957],{},[2783,20029,20030,20032],{},[1908,20031,3811],{},[1969,20033,1990],{},[2530,20035,20036,20038,20040],{},[1908,20037,8472],{},[1969,20039,3819],{},[1969,20041,1990],{},[2783,20043,20044,20046],{},[1908,20045,8626],{},[1969,20047,1990],{},[1912,20049,20050],{"encoding":1914},"\\begin{align*}\n\\mathbb{E}[\\tilde{w}] &= w_0(1+r_f) + \\alpha w_0(\\mu - r_f) \\\\\n\\text{Var}(\\tilde{w}) &= \\alpha^2 w_0^2 \\sigma^2\n\\end{align*}",[1889,20052,20054],{"className":20053,"ariaHidden":1919},[1918],[1889,20055,20057,20061],{"className":20056},[1923],[1889,20058],{"className":20059,"style":20060},[1927],"height:2.7241em;vertical-align:-1.1121em;",[1889,20062,20064],{"className":20063},[1932],[1889,20065,20067,20193],{"className":20066},[8447],[1889,20068,20070],{"className":20069},[8651],[1889,20071,20073,20184],{"className":20072},[2075,2076],[1889,20074,20076,20181],{"className":20075},[2080],[1889,20077,20080,20129],{"className":20078,"style":20079},[2084],"height:1.6121em;",[1889,20081,20083,20086],{"style":20082},"top:-3.7721em;",[1889,20084],{"className":20085,"style":6746},[2092],[1889,20087,20089,20092,20095,20126],{"className":20088},[1932],[1889,20090,5719],{"className":20091},[1932,5355],[1889,20093,5722],{"className":20094},[2061],[1889,20096,20098],{"className":20097},[1932,8700],[1889,20099,20101],{"className":20100},[2075],[1889,20102,20104],{"className":20103},[2080],[1889,20105,20107,20115],{"className":20106,"style":8710},[2084],[1889,20108,20109,20112],{"style":8713},[1889,20110],{"className":20111,"style":6746},[2092],[1889,20113,8472],{"className":20114,"style":8687},[1932,1933],[1889,20116,20117,20120],{"style":8722},[1889,20118],{"className":20119,"style":6746},[2092],[1889,20121,20123],{"className":20122,"style":9650},[8729],[1889,20124,8483],{"className":20125},[1932],[1889,20127,5733],{"className":20128},[2367],[1889,20130,20132,20135],{"style":20131},"top:-2.2479em;",[1889,20133],{"className":20134,"style":6746},[2092],[1889,20136,20138,20144,20147,20178],{"className":20137},[1932],[1889,20139,20141],{"className":20140},[1932,3065],[1889,20142,19602],{"className":20143},[1932],[1889,20145,1961],{"className":20146},[2061],[1889,20148,20150],{"className":20149},[1932,8700],[1889,20151,20153],{"className":20152},[2075],[1889,20154,20156],{"className":20155},[2080],[1889,20157,20159,20167],{"className":20158,"style":8710},[2084],[1889,20160,20161,20164],{"style":8713},[1889,20162],{"className":20163,"style":6746},[2092],[1889,20165,8472],{"className":20166,"style":8687},[1932,1933],[1889,20168,20169,20172],{"style":8722},[1889,20170],{"className":20171,"style":6746},[2092],[1889,20173,20175],{"className":20174,"style":9650},[8729],[1889,20176,8483],{"className":20177},[1932],[1889,20179,2023],{"className":20180},[2367],[1889,20182,2108],{"className":20183},[2107],[1889,20185,20187],{"className":20186},[2080],[1889,20188,20191],{"className":20189,"style":20190},[2084],"height:1.1121em;",[1889,20192],{},[1889,20194,20196],{"className":20195},[8761],[1889,20197,20199,20567],{"className":20198},[2075,2076],[1889,20200,20202,20564],{"className":20201},[2080],[1889,20203,20205,20433],{"className":20204,"style":20079},[2084],[1889,20206,20207,20210],{"style":20082},[1889,20208],{"className":20209,"style":6746},[2092],[1889,20211,20213,20216,20219,20222,20225,20265,20268,20271,20274,20277,20280,20320,20323,20326,20329,20332,20335,20375,20378,20381,20384,20387,20390,20430],{"className":20212},[1932],[1889,20214],{"className":20215},[1932],[1889,20217],{"className":20218,"style":2043},[2042],[1889,20220,1957],{"className":20221},[2047],[1889,20223],{"className":20224,"style":2043},[2042],[1889,20226,20228,20231],{"className":20227},[1932],[1889,20229,8472],{"className":20230,"style":8687},[1932,1933],[1889,20232,20234],{"className":20233},[2071],[1889,20235,20237,20257],{"className":20236},[2075,2076],[1889,20238,20240,20254],{"className":20239},[2080],[1889,20241,20243],{"className":20242,"style":2085},[2084],[1889,20244,20245,20248],{"style":12188},[1889,20246],{"className":20247,"style":2093},[2092],[1889,20249,20251],{"className":20250},[2097,2098,2099,2100],[1889,20252,3819],{"className":20253},[1932,2100],[1889,20255,2108],{"className":20256},[2107],[1889,20258,20260],{"className":20259},[2080],[1889,20261,20263],{"className":20262,"style":2115},[2084],[1889,20264],{},[1889,20266,1961],{"className":20267},[2061],[1889,20269,1971],{"className":20270},[1932],[1889,20272],{"className":20273,"style":4041},[2042],[1889,20275,3910],{"className":20276},[4045],[1889,20278],{"className":20279,"style":4041},[2042],[1889,20281,20283,20286],{"className":20282},[1932],[1889,20284,16887],{"className":20285,"style":16715},[1932,1933],[1889,20287,20289],{"className":20288},[2071],[1889,20290,20292,20312],{"className":20291},[2075,2076],[1889,20293,20295,20309],{"className":20294},[2080],[1889,20296,20298],{"className":20297,"style":16921},[2084],[1889,20299,20300,20303],{"style":16924},[1889,20301],{"className":20302,"style":2093},[2092],[1889,20304,20306],{"className":20305},[2097,2098,2099,2100],[1889,20307,12241],{"className":20308,"style":12322},[1932,1933,2100],[1889,20310,2108],{"className":20311},[2107],[1889,20313,20315],{"className":20314},[2080],[1889,20316,20318],{"className":20317,"style":16943},[2084],[1889,20319],{},[1889,20321,2023],{"className":20322},[2367],[1889,20324],{"className":20325,"style":4041},[2042],[1889,20327,3910],{"className":20328},[4045],[1889,20330],{"className":20331,"style":4041},[2042],[1889,20333,3811],{"className":20334,"style":3842},[1932,1933],[1889,20336,20338,20341],{"className":20337},[1932],[1889,20339,8472],{"className":20340,"style":8687},[1932,1933],[1889,20342,20344],{"className":20343},[2071],[1889,20345,20347,20367],{"className":20346},[2075,2076],[1889,20348,20350,20364],{"className":20349},[2080],[1889,20351,20353],{"className":20352,"style":2085},[2084],[1889,20354,20355,20358],{"style":12188},[1889,20356],{"className":20357,"style":2093},[2092],[1889,20359,20361],{"className":20360},[2097,2098,2099,2100],[1889,20362,3819],{"className":20363},[1932,2100],[1889,20365,2108],{"className":20366},[2107],[1889,20368,20370],{"className":20369},[2080],[1889,20371,20373],{"className":20372,"style":2115},[2084],[1889,20374],{},[1889,20376,1961],{"className":20377},[2061],[1889,20379,17025],{"className":20380},[1932,1933],[1889,20382],{"className":20383,"style":4041},[2042],[1889,20385,3917],{"className":20386},[4045],[1889,20388],{"className":20389,"style":4041},[2042],[1889,20391,20393,20396],{"className":20392},[1932],[1889,20394,16887],{"className":20395,"style":16715},[1932,1933],[1889,20397,20399],{"className":20398},[2071],[1889,20400,20402,20422],{"className":20401},[2075,2076],[1889,20403,20405,20419],{"className":20404},[2080],[1889,20406,20408],{"className":20407,"style":16921},[2084],[1889,20409,20410,20413],{"style":16924},[1889,20411],{"className":20412,"style":2093},[2092],[1889,20414,20416],{"className":20415},[2097,2098,2099,2100],[1889,20417,12241],{"className":20418,"style":12322},[1932,1933,2100],[1889,20420,2108],{"className":20421},[2107],[1889,20423,20425],{"className":20424},[2080],[1889,20426,20428],{"className":20427,"style":16943},[2084],[1889,20429],{},[1889,20431,2023],{"className":20432},[2367],[1889,20434,20435,20438],{"style":20131},[1889,20436],{"className":20437,"style":6746},[2092],[1889,20439,20441,20444,20447,20450,20453,20482,20535],{"className":20440},[1932],[1889,20442],{"className":20443},[1932],[1889,20445],{"className":20446,"style":2043},[2042],[1889,20448,1957],{"className":20449},[2047],[1889,20451],{"className":20452,"style":2043},[2042],[1889,20454,20456,20459],{"className":20455},[1932],[1889,20457,3811],{"className":20458,"style":3842},[1932,1933],[1889,20460,20462],{"className":20461},[2071],[1889,20463,20465],{"className":20464},[2075],[1889,20466,20468],{"className":20467},[2080],[1889,20469,20471],{"className":20470,"style":9057},[2084],[1889,20472,20473,20476],{"style":3045},[1889,20474],{"className":20475,"style":2093},[2092],[1889,20477,20479],{"className":20478},[2097,2098,2099,2100],[1889,20480,1990],{"className":20481},[1932,2100],[1889,20483,20485,20488],{"className":20484},[1932],[1889,20486,8472],{"className":20487,"style":8687},[1932,1933],[1889,20489,20491],{"className":20490},[2071],[1889,20492,20494,20526],{"className":20493},[2075,2076],[1889,20495,20497,20523],{"className":20496},[2080],[1889,20498,20500,20512],{"className":20499,"style":9057},[2084],[1889,20501,20503,20506],{"style":20502},"top:-2.453em;margin-left:-0.0269em;margin-right:0.05em;",[1889,20504],{"className":20505,"style":2093},[2092],[1889,20507,20509],{"className":20508},[2097,2098,2099,2100],[1889,20510,3819],{"className":20511},[1932,2100],[1889,20513,20514,20517],{"style":3045},[1889,20515],{"className":20516,"style":2093},[2092],[1889,20518,20520],{"className":20519},[2097,2098,2099,2100],[1889,20521,1990],{"className":20522},[1932,2100],[1889,20524,2108],{"className":20525},[2107],[1889,20527,20529],{"className":20528},[2080],[1889,20530,20533],{"className":20531,"style":20532},[2084],"height:0.247em;",[1889,20534],{},[1889,20536,20538,20541],{"className":20537},[1932],[1889,20539,8626],{"className":20540,"style":6310},[1932,1933],[1889,20542,20544],{"className":20543},[2071],[1889,20545,20547],{"className":20546},[2075],[1889,20548,20550],{"className":20549},[2080],[1889,20551,20553],{"className":20552,"style":9057},[2084],[1889,20554,20555,20558],{"style":3045},[1889,20556],{"className":20557,"style":2093},[2092],[1889,20559,20561],{"className":20560},[2097,2098,2099,2100],[1889,20562,1990],{"className":20563},[1932,2100],[1889,20565,2108],{"className":20566},[2107],[1889,20568,20570],{"className":20569},[2080],[1889,20571,20573],{"className":20572,"style":20190},[2084],[1889,20574],{},[1798,20576,20577],{},"最优化得：",[1889,20579,20581],{"className":20580},[1938],[1889,20582,20584,20634],{"className":20583},[1892],[1889,20585,20587],{"className":20586},[1896],[1898,20588,20589],{"xmlns":1900,"display":1947},[1902,20590,20591,20631],{},[1905,20592,20593,20599,20601],{},[2783,20594,20595,20597],{},[1908,20596,3811],{},[1955,20598,15587],{},[1955,20600,1957],{},[6567,20602,20603,20615],{},[1905,20604,20605,20607,20609],{},[1908,20606,17025],{},[1955,20608,3917],{},[1963,20610,20611,20613],{},[1908,20612,16887],{},[1908,20614,12241],{},[1905,20616,20617,20619,20625],{},[1908,20618,3811],{},[1963,20620,20621,20623],{},[1908,20622,8472],{},[1969,20624,3819],{},[2783,20626,20627,20629],{},[1908,20628,8626],{},[1969,20630,1990],{},[1912,20632,20633],{"encoding":1914},"\\alpha^* = \\frac{\\mu - r_f}{\\alpha w_0 \\sigma^2}",[1889,20635,20637,20682],{"className":20636,"ariaHidden":1919},[1918],[1889,20638,20640,20644,20673,20676,20679],{"className":20639},[1923],[1889,20641],{"className":20642,"style":20643},[1927],"height:0.7387em;",[1889,20645,20647,20650],{"className":20646},[1932],[1889,20648,3811],{"className":20649,"style":3842},[1932,1933],[1889,20651,20653],{"className":20652},[2071],[1889,20654,20656],{"className":20655},[2075],[1889,20657,20659],{"className":20658},[2080],[1889,20660,20662],{"className":20661,"style":20643},[2084],[1889,20663,20664,20667],{"style":3045},[1889,20665],{"className":20666,"style":2093},[2092],[1889,20668,20670],{"className":20669},[2097,2098,2099,2100],[1889,20671,15587],{"className":20672},[4045,2100],[1889,20674],{"className":20675,"style":2043},[2042],[1889,20677,1957],{"className":20678},[2047],[1889,20680],{"className":20681,"style":2043},[2042],[1889,20683,20685,20689],{"className":20684},[1923],[1889,20686],{"className":20687,"style":20688},[1927],"height:2.0963em;vertical-align:-0.836em;",[1889,20690,20692,20695,20869],{"className":20691},[1932],[1889,20693],{"className":20694},[2061,6726],[1889,20696,20698],{"className":20697},[6567],[1889,20699,20701,20860],{"className":20700},[2075,2076],[1889,20702,20704,20857],{"className":20703},[2080],[1889,20705,20708,20789,20797],{"className":20706,"style":20707},[2084],"height:1.2603em;",[1889,20709,20710,20713],{"style":6742},[1889,20711],{"className":20712,"style":6746},[2092],[1889,20714,20716,20719,20759],{"className":20715},[1932],[1889,20717,3811],{"className":20718,"style":3842},[1932,1933],[1889,20720,20722,20725],{"className":20721},[1932],[1889,20723,8472],{"className":20724,"style":8687},[1932,1933],[1889,20726,20728],{"className":20727},[2071],[1889,20729,20731,20751],{"className":20730},[2075,2076],[1889,20732,20734,20748],{"className":20733},[2080],[1889,20735,20737],{"className":20736,"style":2085},[2084],[1889,20738,20739,20742],{"style":12188},[1889,20740],{"className":20741,"style":2093},[2092],[1889,20743,20745],{"className":20744},[2097,2098,2099,2100],[1889,20746,3819],{"className":20747},[1932,2100],[1889,20749,2108],{"className":20750},[2107],[1889,20752,20754],{"className":20753},[2080],[1889,20755,20757],{"className":20756,"style":2115},[2084],[1889,20758],{},[1889,20760,20762,20765],{"className":20761},[1932],[1889,20763,8626],{"className":20764,"style":6310},[1932,1933],[1889,20766,20768],{"className":20767},[2071],[1889,20769,20771],{"className":20770},[2075],[1889,20772,20774],{"className":20773},[2080],[1889,20775,20778],{"className":20776,"style":20777},[2084],"height:0.7401em;",[1889,20779,20780,20783],{"style":6771},[1889,20781],{"className":20782,"style":2093},[2092],[1889,20784,20786],{"className":20785},[2097,2098,2099,2100],[1889,20787,1990],{"className":20788},[1932,2100],[1889,20790,20791,20794],{"style":6783},[1889,20792],{"className":20793,"style":6746},[2092],[1889,20795],{"className":20796,"style":6791},[6790],[1889,20798,20799,20802],{"style":6794},[1889,20800],{"className":20801,"style":6746},[2092],[1889,20803,20805,20808,20811,20814,20817],{"className":20804},[1932],[1889,20806,17025],{"className":20807},[1932,1933],[1889,20809],{"className":20810,"style":4041},[2042],[1889,20812,3917],{"className":20813},[4045],[1889,20815],{"className":20816,"style":4041},[2042],[1889,20818,20820,20823],{"className":20819},[1932],[1889,20821,16887],{"className":20822,"style":16715},[1932,1933],[1889,20824,20826],{"className":20825},[2071],[1889,20827,20829,20849],{"className":20828},[2075,2076],[1889,20830,20832,20846],{"className":20831},[2080],[1889,20833,20835],{"className":20834,"style":16921},[2084],[1889,20836,20837,20840],{"style":16924},[1889,20838],{"className":20839,"style":2093},[2092],[1889,20841,20843],{"className":20842},[2097,2098,2099,2100],[1889,20844,12241],{"className":20845,"style":12322},[1932,1933,2100],[1889,20847,2108],{"className":20848},[2107],[1889,20850,20852],{"className":20851},[2080],[1889,20853,20855],{"className":20854,"style":16943},[2084],[1889,20856],{},[1889,20858,2108],{"className":20859},[2107],[1889,20861,20863],{"className":20862},[2080],[1889,20864,20867],{"className":20865,"style":20866},[2084],"height:0.836em;",[1889,20868],{},[1889,20870],{"className":20871},[2367,6726],[1798,20873,20874,2704],{},[1884,20875,20876],{},"洞见",[6182,20878,20879,20988,21053,21086],{},[1808,20880,20881,20882,20885,20987],{},"投资比例与",[1884,20883,20884],{},"风险溢价",[1889,20886,20888,20914],{"className":20887},[1892],[1889,20889,20891],{"className":20890},[1896],[1898,20892,20893],{"xmlns":1900},[1902,20894,20895,20911],{},[1905,20896,20897,20899,20901,20903,20909],{},[1955,20898,1961],{"stretchy":1960},[1908,20900,17025],{},[1955,20902,3917],{},[1963,20904,20905,20907],{},[1908,20906,16887],{},[1908,20908,12241],{},[1955,20910,2023],{"stretchy":1960},[1912,20912,20913],{"encoding":1914},"(\\mu - r_f)",[1889,20915,20917,20938],{"className":20916,"ariaHidden":1919},[1918],[1889,20918,20920,20923,20926,20929,20932,20935],{"className":20919},[1923],[1889,20921],{"className":20922,"style":2057},[1927],[1889,20924,1961],{"className":20925},[2061],[1889,20927,17025],{"className":20928},[1932,1933],[1889,20930],{"className":20931,"style":4041},[2042],[1889,20933,3917],{"className":20934},[4045],[1889,20936],{"className":20937,"style":4041},[2042],[1889,20939,20941,20944,20984],{"className":20940},[1923],[1889,20942],{"className":20943,"style":17497},[1927],[1889,20945,20947,20950],{"className":20946},[1932],[1889,20948,16887],{"className":20949,"style":16715},[1932,1933],[1889,20951,20953],{"className":20952},[2071],[1889,20954,20956,20976],{"className":20955},[2075,2076],[1889,20957,20959,20973],{"className":20958},[2080],[1889,20960,20962],{"className":20961,"style":16921},[2084],[1889,20963,20964,20967],{"style":16924},[1889,20965],{"className":20966,"style":2093},[2092],[1889,20968,20970],{"className":20969},[2097,2098,2099,2100],[1889,20971,12241],{"className":20972,"style":12322},[1932,1933,2100],[1889,20974,2108],{"className":20975},[2107],[1889,20977,20979],{"className":20978},[2080],[1889,20980,20982],{"className":20981,"style":16943},[2084],[1889,20983],{},[1889,20985,2023],{"className":20986},[2367],"成正比",[1808,20989,20990,20991,20994,21052],{},"与",[1884,20992,20993],{},"风险",[1889,20995,20997,21014],{"className":20996},[1892],[1889,20998,21000],{"className":20999},[1896],[1898,21001,21002],{"xmlns":1900},[1902,21003,21004,21012],{},[1905,21005,21006],{},[2783,21007,21008,21010],{},[1908,21009,8626],{},[1969,21011,1990],{},[1912,21013,10480],{"encoding":1914},[1889,21015,21017],{"className":21016,"ariaHidden":1919},[1918],[1889,21018,21020,21023],{"className":21019},[1923],[1889,21021],{"className":21022,"style":10490},[1927],[1889,21024,21026,21029],{"className":21025},[1932],[1889,21027,8626],{"className":21028,"style":6310},[1932,1933],[1889,21030,21032],{"className":21031},[2071],[1889,21033,21035],{"className":21034},[2075],[1889,21036,21038],{"className":21037},[2080],[1889,21039,21041],{"className":21040,"style":10490},[2084],[1889,21042,21043,21046],{"style":2825},[1889,21044],{"className":21045,"style":2093},[2092],[1889,21047,21049],{"className":21048},[2097,2098,2099,2100],[1889,21050,1990],{"className":21051},[1932,2100],"成反比",[1808,21054,20990,21055,21058,21052],{},[1884,21056,21057],{},"风险规避系数",[1889,21059,21061,21074],{"className":21060},[1892],[1889,21062,21064],{"className":21063},[1896],[1898,21065,21066],{"xmlns":1900},[1902,21067,21068,21072],{},[1905,21069,21070],{},[1908,21071,3811],{},[1912,21073,11242],{"encoding":1914},[1889,21075,21077],{"className":21076,"ariaHidden":1919},[1918],[1889,21078,21080,21083],{"className":21079},[1923],[1889,21081],{"className":21082,"style":5332},[1927],[1889,21084,3811],{"className":21085,"style":3842},[1932,1933],[1808,21087,20990,21088,21090,21159],{},[1884,21089,17171],{},[1889,21091,21093,21110],{"className":21092},[1892],[1889,21094,21096],{"className":21095},[1896],[1898,21097,21098],{"xmlns":1900},[1902,21099,21100,21108],{},[1905,21101,21102],{},[1963,21103,21104,21106],{},[1908,21105,8472],{},[1969,21107,3819],{},[1912,21109,12158],{"encoding":1914},[1889,21111,21113],{"className":21112,"ariaHidden":1919},[1918],[1889,21114,21116,21119],{"className":21115},[1923],[1889,21117],{"className":21118,"style":2475},[1927],[1889,21120,21122,21125],{"className":21121},[1932],[1889,21123,8472],{"className":21124,"style":8687},[1932,1933],[1889,21126,21128],{"className":21127},[2071],[1889,21129,21131,21151],{"className":21130},[2075,2076],[1889,21132,21134,21148],{"className":21133},[2080],[1889,21135,21137],{"className":21136,"style":2085},[2084],[1889,21138,21139,21142],{"style":12188},[1889,21140],{"className":21141,"style":2093},[2092],[1889,21143,21145],{"className":21144},[2097,2098,2099,2100],[1889,21146,3819],{"className":21147},[1932,2100],[1889,21149,2108],{"className":21150},[2107],[1889,21152,21154],{"className":21153},[2080],[1889,21155,21157],{"className":21156,"style":2115},[2084],[1889,21158],{},"成反比（CARA的特殊性质）",[1877,21161,21163],{"id":21162},"_44-均值-方差分析","4.4 均值-方差分析",[1798,21165,21166,21167,21359],{},"如果效用函数是二次的：",[1889,21168,21170,21208],{"className":21169},[1892],[1889,21171,21173],{"className":21172},[1896],[1898,21174,21175],{"xmlns":1900},[1902,21176,21177,21205],{},[1905,21178,21179,21181,21183,21185,21187,21189,21191,21193,21199],{},[1908,21180,5308],{},[1955,21182,1961],{"stretchy":1960},[1908,21184,8472],{},[1955,21186,2023],{"stretchy":1960},[1955,21188,1957],{},[1908,21190,8472],{},[1955,21192,3917],{},[6567,21194,21195,21197],{},[1908,21196,6292],{},[1969,21198,1990],{},[2783,21200,21201,21203],{},[1908,21202,8472],{},[1969,21204,1990],{},[1912,21206,21207],{"encoding":1914},"u(w) = w - \\frac{b}{2}w^2",[1889,21209,21211,21238,21256],{"className":21210,"ariaHidden":1919},[1918],[1889,21212,21214,21217,21220,21223,21226,21229,21232,21235],{"className":21213},[1923],[1889,21215],{"className":21216,"style":2057},[1927],[1889,21218,5308],{"className":21219},[1932,1933],[1889,21221,1961],{"className":21222},[2061],[1889,21224,8472],{"className":21225,"style":8687},[1932,1933],[1889,21227,2023],{"className":21228},[2367],[1889,21230],{"className":21231,"style":2043},[2042],[1889,21233,1957],{"className":21234},[2047],[1889,21236],{"className":21237,"style":2043},[2042],[1889,21239,21241,21244,21247,21250,21253],{"className":21240},[1923],[1889,21242],{"className":21243,"style":6326},[1927],[1889,21245,8472],{"className":21246,"style":8687},[1932,1933],[1889,21248],{"className":21249,"style":4041},[2042],[1889,21251,3917],{"className":21252},[4045],[1889,21254],{"className":21255,"style":4041},[2042],[1889,21257,21259,21262,21330],{"className":21258},[1923],[1889,21260],{"className":21261,"style":11611},[1927],[1889,21263,21265,21268,21327],{"className":21264},[1932],[1889,21266],{"className":21267},[2061,6726],[1889,21269,21271],{"className":21270},[6567],[1889,21272,21274,21319],{"className":21273},[2075,2076],[1889,21275,21277,21316],{"className":21276},[2080],[1889,21278,21280,21294,21302],{"className":21279,"style":11630},[2084],[1889,21281,21282,21285],{"style":11372},[1889,21283],{"className":21284,"style":6746},[2092],[1889,21286,21288],{"className":21287},[2097,2098,2099,2100],[1889,21289,21291],{"className":21290},[1932,2100],[1889,21292,1990],{"className":21293},[1932,2100],[1889,21295,21296,21299],{"style":6783},[1889,21297],{"className":21298,"style":6746},[2092],[1889,21300],{"className":21301,"style":6791},[6790],[1889,21303,21304,21307],{"style":11402},[1889,21305],{"className":21306,"style":6746},[2092],[1889,21308,21310],{"className":21309},[2097,2098,2099,2100],[1889,21311,21313],{"className":21312},[1932,2100],[1889,21314,6292],{"className":21315},[1932,1933,2100],[1889,21317,2108],{"className":21318},[2107],[1889,21320,21322],{"className":21321},[2080],[1889,21323,21325],{"className":21324,"style":11676},[2084],[1889,21326],{},[1889,21328],{"className":21329},[2367,6726],[1889,21331,21333,21336],{"className":21332},[1932],[1889,21334,8472],{"className":21335,"style":8687},[1932,1933],[1889,21337,21339],{"className":21338},[2071],[1889,21340,21342],{"className":21341},[2075],[1889,21343,21345],{"className":21344},[2080],[1889,21346,21348],{"className":21347,"style":10490},[2084],[1889,21349,21350,21353],{"style":2825},[1889,21351],{"className":21352,"style":2093},[2092],[1889,21354,21356],{"className":21355},[2097,2098,2099,2100],[1889,21357,1990],{"className":21358},[1932,2100],"，或者收益率服从正态分布，则投资者的偏好可以完全由投资组合的均值和方差刻画。",[1798,21361,21362,2704],{},[1884,21363,6189],{},[1889,21365,21367],{"className":21366},[1938],[1889,21368,21370,21476],{"className":21369},[1892],[1889,21371,21373],{"className":21372},[1896],[1898,21374,21375],{"xmlns":1900,"display":1947},[1902,21376,21377,21473],{},[1905,21378,21379,21381,21383,21385,21387,21393,21395,21397,21399,21401,21403,21409,21411,21413,21419,21421,21423,21433,21435,21437,21443,21445,21451,21453,21461,21463,21471],{},[1908,21380,5719],{"mathvariant":5313},[1955,21382,5722],{"stretchy":1960},[1908,21384,5308],{},[1955,21386,1961],{"stretchy":1960},[8476,21388,21389,21391],{"accent":1919},[1908,21390,8472],{},[1955,21392,8483],{},[1955,21394,2023],{"stretchy":1960},[1955,21396,5733],{"stretchy":1960},[1955,21398,1957],{},[1908,21400,5719],{"mathvariant":5313},[1955,21402,5722],{"stretchy":1960},[8476,21404,21405,21407],{"accent":1919},[1908,21406,8472],{},[1955,21408,8483],{},[1955,21410,5733],{"stretchy":1960},[1955,21412,3917],{},[6567,21414,21415,21417],{},[1908,21416,6292],{},[1969,21418,1990],{},[1908,21420,5719],{"mathvariant":5313},[1955,21422,5722],{"stretchy":1960},[2783,21424,21425,21431],{},[8476,21426,21427,21429],{"accent":1919},[1908,21428,8472],{},[1955,21430,8483],{},[1969,21432,1990],{},[1955,21434,5733],{"stretchy":1960},[1955,21436,1957],{},[1963,21438,21439,21441],{},[1908,21440,17025],{},[1908,21442,8472],{},[1955,21444,3917],{},[6567,21446,21447,21449],{},[1908,21448,6292],{},[1969,21450,1990],{},[1955,21452,1961],{"stretchy":1960},[2530,21454,21455,21457,21459],{},[1908,21456,17025],{},[1908,21458,8472],{},[1969,21460,1990],{},[1955,21462,3910],{},[2530,21464,21465,21467,21469],{},[1908,21466,8626],{},[1908,21468,8472],{},[1969,21470,1990],{},[1955,21472,2023],{"stretchy":1960},[1912,21474,21475],{"encoding":1914},"\\mathbb{E}[u(\\tilde{w})] = \\mathbb{E}[\\tilde{w}] - \\frac{b}{2}\\mathbb{E}[\\tilde{w}^2] = \\mu_w - \\frac{b}{2}(\\mu_w^2 + \\sigma_w^2)",[1889,21477,21479,21540,21595,21739,21795,21927],{"className":21478,"ariaHidden":1919},[1918],[1889,21480,21482,21485,21488,21491,21494,21497,21528,21531,21534,21537],{"className":21481},[1923],[1889,21483],{"className":21484,"style":2057},[1927],[1889,21486,5719],{"className":21487},[1932,5355],[1889,21489,5722],{"className":21490},[2061],[1889,21492,5308],{"className":21493},[1932,1933],[1889,21495,1961],{"className":21496},[2061],[1889,21498,21500],{"className":21499},[1932,8700],[1889,21501,21503],{"className":21502},[2075],[1889,21504,21506],{"className":21505},[2080],[1889,21507,21509,21517],{"className":21508,"style":8710},[2084],[1889,21510,21511,21514],{"style":8713},[1889,21512],{"className":21513,"style":6746},[2092],[1889,21515,8472],{"className":21516,"style":8687},[1932,1933],[1889,21518,21519,21522],{"style":8722},[1889,21520],{"className":21521,"style":6746},[2092],[1889,21523,21525],{"className":21524,"style":9650},[8729],[1889,21526,8483],{"className":21527},[1932],[1889,21529,5972],{"className":21530},[2367],[1889,21532],{"className":21533,"style":2043},[2042],[1889,21535,1957],{"className":21536},[2047],[1889,21538],{"className":21539,"style":2043},[2042],[1889,21541,21543,21546,21549,21552,21583,21586,21589,21592],{"className":21542},[1923],[1889,21544],{"className":21545,"style":2057},[1927],[1889,21547,5719],{"className":21548},[1932,5355],[1889,21550,5722],{"className":21551},[2061],[1889,21553,21555],{"className":21554},[1932,8700],[1889,21556,21558],{"className":21557},[2075],[1889,21559,21561],{"className":21560},[2080],[1889,21562,21564,21572],{"className":21563,"style":8710},[2084],[1889,21565,21566,21569],{"style":8713},[1889,21567],{"className":21568,"style":6746},[2092],[1889,21570,8472],{"className":21571,"style":8687},[1932,1933],[1889,21573,21574,21577],{"style":8722},[1889,21575],{"className":21576,"style":6746},[2092],[1889,21578,21580],{"className":21579,"style":9650},[8729],[1889,21581,8483],{"className":21582},[1932],[1889,21584,5733],{"className":21585},[2367],[1889,21587],{"className":21588,"style":4041},[2042],[1889,21590,3917],{"className":21591},[4045],[1889,21593],{"className":21594,"style":4041},[2042],[1889,21596,21598,21602,21664,21667,21670,21727,21730,21733,21736],{"className":21597},[1923],[1889,21599],{"className":21600,"style":21601},[1927],"height:2.0574em;vertical-align:-0.686em;",[1889,21603,21605,21608,21661],{"className":21604},[1932],[1889,21606],{"className":21607},[2061,6726],[1889,21609,21611],{"className":21610},[6567],[1889,21612,21614,21653],{"className":21613},[2075,2076],[1889,21615,21617,21650],{"className":21616},[2080],[1889,21618,21620,21631,21639],{"className":21619,"style":7534},[2084],[1889,21621,21622,21625],{"style":6742},[1889,21623],{"className":21624,"style":6746},[2092],[1889,21626,21628],{"className":21627},[1932],[1889,21629,1990],{"className":21630},[1932],[1889,21632,21633,21636],{"style":6783},[1889,21634],{"className":21635,"style":6746},[2092],[1889,21637],{"className":21638,"style":6791},[6790],[1889,21640,21641,21644],{"style":6794},[1889,21642],{"className":21643,"style":6746},[2092],[1889,21645,21647],{"className":21646},[1932],[1889,21648,6292],{"className":21649},[1932,1933],[1889,21651,2108],{"className":21652},[2107],[1889,21654,21656],{"className":21655},[2080],[1889,21657,21659],{"className":21658,"style":6813},[2084],[1889,21660],{},[1889,21662],{"className":21663},[2367,6726],[1889,21665,5719],{"className":21666},[1932,5355],[1889,21668,5722],{"className":21669},[2061],[1889,21671,21673,21704],{"className":21672},[1932],[1889,21674,21676],{"className":21675},[1932,8700],[1889,21677,21679],{"className":21678},[2075],[1889,21680,21682],{"className":21681},[2080],[1889,21683,21685,21693],{"className":21684,"style":8710},[2084],[1889,21686,21687,21690],{"style":8713},[1889,21688],{"className":21689,"style":6746},[2092],[1889,21691,8472],{"className":21692,"style":8687},[1932,1933],[1889,21694,21695,21698],{"style":8722},[1889,21696],{"className":21697,"style":6746},[2092],[1889,21699,21701],{"className":21700,"style":9650},[8729],[1889,21702,8483],{"className":21703},[1932],[1889,21705,21707],{"className":21706},[2071],[1889,21708,21710],{"className":21709},[2075],[1889,21711,21713],{"className":21712},[2080],[1889,21714,21716],{"className":21715,"style":9057},[2084],[1889,21717,21718,21721],{"style":3045},[1889,21719],{"className":21720,"style":2093},[2092],[1889,21722,21724],{"className":21723},[2097,2098,2099,2100],[1889,21725,1990],{"className":21726},[1932,2100],[1889,21728,5733],{"className":21729},[2367],[1889,21731],{"className":21732,"style":2043},[2042],[1889,21734,1957],{"className":21735},[2047],[1889,21737],{"className":21738,"style":2043},[2042],[1889,21740,21742,21746,21786,21789,21792],{"className":21741},[1923],[1889,21743],{"className":21744,"style":21745},[1927],"height:0.7778em;vertical-align:-0.1944em;",[1889,21747,21749,21752],{"className":21748},[1932],[1889,21750,17025],{"className":21751},[1932,1933],[1889,21753,21755],{"className":21754},[2071],[1889,21756,21758,21778],{"className":21757},[2075,2076],[1889,21759,21761,21775],{"className":21760},[2080],[1889,21762,21764],{"className":21763,"style":2295},[2084],[1889,21765,21766,21769],{"style":2088},[1889,21767],{"className":21768,"style":2093},[2092],[1889,21770,21772],{"className":21771},[2097,2098,2099,2100],[1889,21773,8472],{"className":21774,"style":8687},[1932,1933,2100],[1889,21776,2108],{"className":21777},[2107],[1889,21779,21781],{"className":21780},[2080],[1889,21782,21784],{"className":21783,"style":2115},[2084],[1889,21785],{},[1889,21787],{"className":21788,"style":4041},[2042],[1889,21790,3917],{"className":21791},[4045],[1889,21793],{"className":21794,"style":4041},[2042],[1889,21796,21798,21801,21863,21866,21918,21921,21924],{"className":21797},[1923],[1889,21799],{"className":21800,"style":21601},[1927],[1889,21802,21804,21807,21860],{"className":21803},[1932],[1889,21805],{"className":21806},[2061,6726],[1889,21808,21810],{"className":21809},[6567],[1889,21811,21813,21852],{"className":21812},[2075,2076],[1889,21814,21816,21849],{"className":21815},[2080],[1889,21817,21819,21830,21838],{"className":21818,"style":7534},[2084],[1889,21820,21821,21824],{"style":6742},[1889,21822],{"className":21823,"style":6746},[2092],[1889,21825,21827],{"className":21826},[1932],[1889,21828,1990],{"className":21829},[1932],[1889,21831,21832,21835],{"style":6783},[1889,21833],{"className":21834,"style":6746},[2092],[1889,21836],{"className":21837,"style":6791},[6790],[1889,21839,21840,21843],{"style":6794},[1889,21841],{"className":21842,"style":6746},[2092],[1889,21844,21846],{"className":21845},[1932],[1889,21847,6292],{"className":21848},[1932,1933],[1889,21850,2108],{"className":21851},[2107],[1889,21853,21855],{"className":21854},[2080],[1889,21856,21858],{"className":21857,"style":6813},[2084],[1889,21859],{},[1889,21861],{"className":21862},[2367,6726],[1889,21864,1961],{"className":21865},[2061],[1889,21867,21869,21872],{"className":21868},[1932],[1889,21870,17025],{"className":21871},[1932,1933],[1889,21873,21875],{"className":21874},[2071],[1889,21876,21878,21910],{"className":21877},[2075,2076],[1889,21879,21881,21907],{"className":21880},[2080],[1889,21882,21884,21896],{"className":21883,"style":9057},[2084],[1889,21885,21887,21890],{"style":21886},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1889,21888],{"className":21889,"style":2093},[2092],[1889,21891,21893],{"className":21892},[2097,2098,2099,2100],[1889,21894,8472],{"className":21895,"style":8687},[1932,1933,2100],[1889,21897,21898,21901],{"style":3045},[1889,21899],{"className":21900,"style":2093},[2092],[1889,21902,21904],{"className":21903},[2097,2098,2099,2100],[1889,21905,1990],{"className":21906},[1932,2100],[1889,21908,2108],{"className":21909},[2107],[1889,21911,21913],{"className":21912},[2080],[1889,21914,21916],{"className":21915,"style":20532},[2084],[1889,21917],{},[1889,21919],{"className":21920,"style":4041},[2042],[1889,21922,3910],{"className":21923},[4045],[1889,21925],{"className":21926,"style":4041},[2042],[1889,21928,21930,21934,21986],{"className":21929},[1923],[1889,21931],{"className":21932,"style":21933},[1927],"height:1.1141em;vertical-align:-0.25em;",[1889,21935,21937,21940],{"className":21936},[1932],[1889,21938,8626],{"className":21939,"style":6310},[1932,1933],[1889,21941,21943],{"className":21942},[2071],[1889,21944,21946,21978],{"className":21945},[2075,2076],[1889,21947,21949,21975],{"className":21948},[2080],[1889,21950,21952,21964],{"className":21951,"style":9057},[2084],[1889,21953,21955,21958],{"style":21954},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[1889,21956],{"className":21957,"style":2093},[2092],[1889,21959,21961],{"className":21960},[2097,2098,2099,2100],[1889,21962,8472],{"className":21963,"style":8687},[1932,1933,2100],[1889,21965,21966,21969],{"style":3045},[1889,21967],{"className":21968,"style":2093},[2092],[1889,21970,21972],{"className":21971},[2097,2098,2099,2100],[1889,21973,1990],{"className":21974},[1932,2100],[1889,21976,2108],{"className":21977},[2107],[1889,21979,21981],{"className":21980},[2080],[1889,21982,21984],{"className":21983,"style":20532},[2084],[1889,21985],{},[1889,21987,2023],{"className":21988},[2367],[1798,21990,21991],{},"这简化为均值-方差效用：",[1889,21993,21995],{"className":21994},[1938],[1889,21996,21998,22045],{"className":21997},[1892],[1889,21999,22001],{"className":22000},[1896],[1898,22002,22003],{"xmlns":1900,"display":1947},[1902,22004,22005,22042],{},[1905,22006,22007,22010,22012,22014,22016,22022,22024,22026,22028,22030,22036],{},[1908,22008,22009],{},"V",[1955,22011,1961],{"stretchy":1960},[1908,22013,17025],{},[1955,22015,1974],{"separator":1919},[2783,22017,22018,22020],{},[1908,22019,8626],{},[1969,22021,1990],{},[1955,22023,2023],{"stretchy":1960},[1955,22025,1957],{},[1908,22027,17025],{},[1955,22029,3917],{},[6567,22031,22032,22034],{},[1908,22033,6292],{},[1969,22035,1990],{},[2783,22037,22038,22040],{},[1908,22039,8626],{},[1969,22041,1990],{},[1912,22043,22044],{"encoding":1914},"V(\\mu, \\sigma^2) = \\mu - \\frac{b}{2}\\sigma^2",[1889,22046,22048,22110,22128],{"className":22047,"ariaHidden":1919},[1918],[1889,22049,22051,22054,22057,22060,22063,22066,22069,22098,22101,22104,22107],{"className":22050},[1923],[1889,22052],{"className":22053,"style":21933},[1927],[1889,22055,22009],{"className":22056,"style":4041},[1932,1933],[1889,22058,1961],{"className":22059},[2061],[1889,22061,17025],{"className":22062},[1932,1933],[1889,22064,1974],{"className":22065},[2121],[1889,22067],{"className":22068,"style":2125},[2042],[1889,22070,22072,22075],{"className":22071},[1932],[1889,22073,8626],{"className":22074,"style":6310},[1932,1933],[1889,22076,22078],{"className":22077},[2071],[1889,22079,22081],{"className":22080},[2075],[1889,22082,22084],{"className":22083},[2080],[1889,22085,22087],{"className":22086,"style":9057},[2084],[1889,22088,22089,22092],{"style":3045},[1889,22090],{"className":22091,"style":2093},[2092],[1889,22093,22095],{"className":22094},[2097,2098,2099,2100],[1889,22096,1990],{"className":22097},[1932,2100],[1889,22099,2023],{"className":22100},[2367],[1889,22102],{"className":22103,"style":2043},[2042],[1889,22105,1957],{"className":22106},[2047],[1889,22108],{"className":22109,"style":2043},[2042],[1889,22111,22113,22116,22119,22122,22125],{"className":22112},[1923],[1889,22114],{"className":22115,"style":21745},[1927],[1889,22117,17025],{"className":22118},[1932,1933],[1889,22120],{"className":22121,"style":4041},[2042],[1889,22123,3917],{"className":22124},[4045],[1889,22126],{"className":22127,"style":4041},[2042],[1889,22129,22131,22134,22196],{"className":22130},[1923],[1889,22132],{"className":22133,"style":21601},[1927],[1889,22135,22137,22140,22193],{"className":22136},[1932],[1889,22138],{"className":22139},[2061,6726],[1889,22141,22143],{"className":22142},[6567],[1889,22144,22146,22185],{"className":22145},[2075,2076],[1889,22147,22149,22182],{"className":22148},[2080],[1889,22150,22152,22163,22171],{"className":22151,"style":7534},[2084],[1889,22153,22154,22157],{"style":6742},[1889,22155],{"className":22156,"style":6746},[2092],[1889,22158,22160],{"className":22159},[1932],[1889,22161,1990],{"className":22162},[1932],[1889,22164,22165,22168],{"style":6783},[1889,22166],{"className":22167,"style":6746},[2092],[1889,22169],{"className":22170,"style":6791},[6790],[1889,22172,22173,22176],{"style":6794},[1889,22174],{"className":22175,"style":6746},[2092],[1889,22177,22179],{"className":22178},[1932],[1889,22180,6292],{"className":22181},[1932,1933],[1889,22183,2108],{"className":22184},[2107],[1889,22186,22188],{"className":22187},[2080],[1889,22189,22191],{"className":22190,"style":6813},[2084],[1889,22192],{},[1889,22194],{"className":22195},[2367,6726],[1889,22197,22199,22202],{"className":22198},[1932],[1889,22200,8626],{"className":22201,"style":6310},[1932,1933],[1889,22203,22205],{"className":22204},[2071],[1889,22206,22208],{"className":22207},[2075],[1889,22209,22211],{"className":22210},[2080],[1889,22212,22214],{"className":22213,"style":9057},[2084],[1889,22215,22216,22219],{"style":3045},[1889,22217],{"className":22218,"style":2093},[2092],[1889,22220,22222],{"className":22221},[2097,2098,2099,2100],[1889,22223,1990],{"className":22224},[1932,2100],[1798,22226,22227,22230],{},[1884,22228,22229],{},"马科维茨投资组合理论","的基础！",[1870,22232],{},[1794,22234,22236],{"id":22235},"_5-前景理论-prospect-theory","5. 前景理论 (Prospect Theory)",[1877,22238,22240],{"id":22239},"_51-期望效用理论的实证挑战","5.1 期望效用理论的实证挑战",[1798,22242,22243,2704],{},[1884,22244,22245],{},"阿莱悖论 (Allais Paradox, 1953)",[1798,22247,22248],{},"选择1:",[1805,22250,22251,22254],{},[1808,22252,22253],{},"A: 确定获得100万",[1808,22255,22256],{},"B: 10%概率获得500万，89%概率获得100万，1%概率什么都没有",[1798,22258,22259],{},"选择2:",[1805,22261,22262,22265],{},[1808,22263,22264],{},"C: 11%概率获得100万，89%概率什么都没有",[1808,22266,22267],{},"D: 10%概率获得500万，90%概率什么都没有",[1798,22269,22270,22273],{},[1884,22271,22272],{},"实证发现",": 大多数人选A和D，但这违反了独立性公理！",[1877,22275,22277],{"id":22276},"_52-前景理论的核心要素","5.2 前景理论的核心要素",[1798,22279,22280,22283],{},[1884,22281,22282],{},"卡尼曼和特沃斯基 (Kahneman & Tversky, 1979)"," 提出前景理论来解释这些\"异常\"。",[1798,22285,22286,2704],{},[1884,22287,22288],{},"关键特征",[6182,22290,22291,22804,23188],{},[1808,22292,22293,22296,22297,22645,22648,22649,22700,22701,22704,22705,16675,22779,22781,2704,22783],{},[1884,22294,22295],{},"价值函数 (Value Function)"," 而非效用函数:",[1889,22298,22300],{"className":22299},[1938],[1889,22301,22303,22396],{"className":22302},[1892],[1889,22304,22306],{"className":22305},[1896],[1898,22307,22308],{"xmlns":1900,"display":1947},[1902,22309,22310,22393],{},[1905,22311,22312,22314,22316,22318,22320,22322],{},[1908,22313,6283],{},[1955,22315,1961],{"stretchy":1960},[1908,22317,1967],{},[1955,22319,2023],{"stretchy":1960},[1955,22321,1957],{},[1905,22323,22324,22327],{},[1955,22325,22326],{"fence":1919},"{",[8447,22328,22331,22355],{"rowspacing":22329,"columnalign":22330,"columnspacing":2958},"0.36em","left left",[8452,22332,22333,22343],{},[8455,22334,22335],{},[8458,22336,22337],{"scriptlevel":3819,"displaystyle":1960},[2783,22338,22339,22341],{},[1908,22340,1967],{},[1908,22342,3811],{},[8455,22344,22345],{},[8458,22346,22347],{"scriptlevel":3819,"displaystyle":1960},[1905,22348,22349,22351,22353],{},[1908,22350,1967],{},[1955,22352,6082],{},[1969,22354,3819],{},[8452,22356,22357,22381],{},[8455,22358,22359],{},[8458,22360,22361],{"scriptlevel":3819,"displaystyle":1960},[1905,22362,22363,22365,22368,22370,22372,22374],{},[1955,22364,3917],{},[1908,22366,22367],{},"λ",[1955,22369,1961],{"stretchy":1960},[1955,22371,3917],{},[1908,22373,1967],{},[2783,22375,22376,22378],{},[1955,22377,2023],{"stretchy":1960},[1908,22379,22380],{},"β",[8455,22382,22383],{},[8458,22384,22385],{"scriptlevel":3819,"displaystyle":1960},[1905,22386,22387,22389,22391],{},[1908,22388,1967],{},[1955,22390,8012],{},[1969,22392,3819],{},[1912,22394,22395],{"encoding":1914},"v(x) = \\begin{cases}\nx^\\alpha & x \\ge 0 \\\\\n-\\lambda(-x)^\\beta & x \u003C 0\n\\end{cases}",[1889,22397,22399,22426],{"className":22398,"ariaHidden":1919},[1918],[1889,22400,22402,22405,22408,22411,22414,22417,22420,22423],{"className":22401},[1923],[1889,22403],{"className":22404,"style":2057},[1927],[1889,22406,6283],{"className":22407,"style":6310},[1932,1933],[1889,22409,1961],{"className":22410},[2061],[1889,22412,1967],{"className":22413},[1932,1933],[1889,22415,2023],{"className":22416},[2367],[1889,22418],{"className":22419,"style":2043},[2042],[1889,22421,1957],{"className":22422},[2047],[1889,22424],{"className":22425,"style":2043},[2042],[1889,22427,22429,22433],{"className":22428},[1923],[1889,22430],{"className":22431,"style":22432},[1927],"height:3em;vertical-align:-1.25em;",[1889,22434,22436,22443,22642],{"className":22435},[2267],[1889,22437,22439],{"className":22438,"style":19708},[2061,19707],[1889,22440,22326],{"className":22441},[19712,22442],"size4",[1889,22444,22446],{"className":22445},[1932],[1889,22447,22449,22568,22573],{"className":22448},[8447],[1889,22450,22452],{"className":22451},[8761],[1889,22453,22455,22559],{"className":22454},[2075,2076],[1889,22456,22458,22556],{"className":22457},[2080],[1889,22459,22462,22501],{"className":22460,"style":22461},[2084],"height:1.69em;",[1889,22463,22465,22469],{"style":22464},"top:-3.69em;",[1889,22466],{"className":22467,"style":22468},[2092],"height:3.008em;",[1889,22470,22472],{"className":22471},[1932],[1889,22473,22475,22478],{"className":22474},[1932],[1889,22476,1967],{"className":22477},[1932,1933],[1889,22479,22481],{"className":22480},[2071],[1889,22482,22484],{"className":22483},[2075],[1889,22485,22487],{"className":22486},[2080],[1889,22488,22490],{"className":22489,"style":6489},[2084],[1889,22491,22492,22495],{"style":2825},[1889,22493],{"className":22494,"style":2093},[2092],[1889,22496,22498],{"className":22497},[2097,2098,2099,2100],[1889,22499,3811],{"className":22500,"style":3842},[1932,1933,2100],[1889,22502,22504,22507],{"style":22503},"top:-2.25em;",[1889,22505],{"className":22506,"style":22468},[2092],[1889,22508,22510,22513,22516,22519,22522,22525],{"className":22509},[1932],[1889,22511,3917],{"className":22512},[1932],[1889,22514,22367],{"className":22515},[1932,1933],[1889,22517,1961],{"className":22518},[2061],[1889,22520,3917],{"className":22521},[1932],[1889,22523,1967],{"className":22524},[1932,1933],[1889,22526,22528,22531],{"className":22527},[2367],[1889,22529,2023],{"className":22530},[2367],[1889,22532,22534],{"className":22533},[2071],[1889,22535,22537],{"className":22536},[2075],[1889,22538,22540],{"className":22539},[2080],[1889,22541,22544],{"className":22542,"style":22543},[2084],"height:0.8491em;",[1889,22545,22546,22549],{"style":2825},[1889,22547],{"className":22548,"style":2093},[2092],[1889,22550,22552],{"className":22551},[2097,2098,2099,2100],[1889,22553,22380],{"className":22554,"style":22555},[1932,1933,2100],"margin-right:0.0528em;",[1889,22557,2108],{"className":22558},[2107],[1889,22560,22562],{"className":22561},[2080],[1889,22563,22566],{"className":22564,"style":22565},[2084],"height:1.19em;",[1889,22567],{},[1889,22569],{"className":22570,"style":22572},[22571],"arraycolsep","width:1em;",[1889,22574,22576],{"className":22575},[8761],[1889,22577,22579,22634],{"className":22578},[2075,2076],[1889,22580,22582,22631],{"className":22581},[2080],[1889,22583,22585,22608],{"className":22584,"style":22461},[2084],[1889,22586,22587,22590],{"style":22464},[1889,22588],{"className":22589,"style":22468},[2092],[1889,22591,22593,22596,22599,22602,22605],{"className":22592},[1932],[1889,22594,1967],{"className":22595},[1932,1933],[1889,22597],{"className":22598,"style":2043},[2042],[1889,22600,6082],{"className":22601},[2047],[1889,22603],{"className":22604,"style":2043},[2042],[1889,22606,3819],{"className":22607},[1932],[1889,22609,22610,22613],{"style":22503},[1889,22611],{"className":22612,"style":22468},[2092],[1889,22614,22616,22619,22622,22625,22628],{"className":22615},[1932],[1889,22617,1967],{"className":22618},[1932,1933],[1889,22620],{"className":22621,"style":2043},[2042],[1889,22623,8012],{"className":22624},[2047],[1889,22626],{"className":22627,"style":2043},[2042],[1889,22629,3819],{"className":22630},[1932],[1889,22632,2108],{"className":22633},[2107],[1889,22635,22637],{"className":22636},[2080],[1889,22638,22640],{"className":22639,"style":22565},[2084],[1889,22641],{},[1889,22643],{"className":22644},[2367,6726],[22646,22647],"br",{},"其中",[1889,22650,22652,22670],{"className":22651},[1892],[1889,22653,22655],{"className":22654},[1896],[1898,22656,22657],{"xmlns":1900},[1902,22658,22659,22667],{},[1905,22660,22661,22663,22665],{},[1908,22662,22367],{},[1955,22664,6369],{},[1969,22666,1971],{},[1912,22668,22669],{"encoding":1914},"\\lambda > 1",[1889,22671,22673,22691],{"className":22672,"ariaHidden":1919},[1918],[1889,22674,22676,22679,22682,22685,22688],{"className":22675},[1923],[1889,22677],{"className":22678,"style":6384},[1927],[1889,22680,22367],{"className":22681},[1932,1933],[1889,22683],{"className":22684,"style":2043},[2042],[1889,22686,6369],{"className":22687},[2047],[1889,22689],{"className":22690,"style":2043},[2042],[1889,22692,22694,22697],{"className":22693},[1923],[1889,22695],{"className":22696,"style":2694},[1927],[1889,22698,1971],{"className":22699},[1932],"是",[1884,22702,22703],{},"损失规避系数","（通常",[1889,22706,22708,22731],{"className":22707},[1892],[1889,22709,22711],{"className":22710},[1896],[1898,22712,22713],{"xmlns":1900},[1902,22714,22715,22728],{},[1905,22716,22717,22719,22721,22723,22725],{},[1908,22718,22367],{},[1955,22720,7183],{},[1969,22722,1990],{},[1955,22724,3917],{},[1969,22726,22727],{},"2.5",[1912,22729,22730],{"encoding":1914},"\\lambda \\approx 2-2.5",[1889,22732,22734,22752,22770],{"className":22733,"ariaHidden":1919},[1918],[1889,22735,22737,22740,22743,22746,22749],{"className":22736},[1923],[1889,22738],{"className":22739,"style":6345},[1927],[1889,22741,22367],{"className":22742},[1932,1933],[1889,22744],{"className":22745,"style":2043},[2042],[1889,22747,7183],{"className":22748},[2047],[1889,22750],{"className":22751,"style":2043},[2042],[1889,22753,22755,22758,22761,22764,22767],{"className":22754},[1923],[1889,22756],{"className":22757,"style":12913},[1927],[1889,22759,1990],{"className":22760},[1932],[1889,22762],{"className":22763,"style":4041},[2042],[1889,22765,3917],{"className":22766},[4045],[1889,22768],{"className":22769,"style":4041},[2042],[1889,22771,22773,22776],{"className":22772},[1923],[1889,22774],{"className":22775,"style":2694},[1927],[1889,22777,22727],{"className":22778},[1932],[22646,22780],{},[1884,22782,10992],{},[1805,22784,22785,22792,22795,22798],{},[1808,22786,22787,22788,22791],{},"定义在",[1884,22789,22790],{},"变化","（相对于参照点）而非绝对财富上",[1808,22793,22794],{},"收益区域凹（风险规避）",[1808,22796,22797],{},"损失区域凸（风险寻求）",[1808,22799,22800,22803],{},[1884,22801,22802],{},"损失规避",": 损失的痛苦大于等量收益的快乐",[1808,22805,22806,22809,22810,23133,22648,23135,2698],{},[1884,22807,22808],{},"概率权重函数",":\n人们系统性地高估小概率事件，低估大概率事件。",[1889,22811,22813],{"className":22812},[1938],[1889,22814,22816,22884],{"className":22815},[1892],[1889,22817,22819],{"className":22818},[1896],[1898,22820,22821],{"xmlns":1900,"display":1947},[1902,22822,22823,22881],{},[1905,22824,22825,22827,22829,22831,22833,22835],{},[1908,22826,8472],{},[1955,22828,1961],{"stretchy":1960},[1908,22830,1798],{},[1955,22832,2023],{"stretchy":1960},[1955,22834,1957],{},[6567,22836,22837,22843],{},[2783,22838,22839,22841],{},[1908,22840,1798],{},[1908,22842,11329],{},[1905,22844,22845,22847,22853,22855,22857,22859,22861,22863,22869],{},[1955,22846,1961],{"stretchy":1960},[2783,22848,22849,22851],{},[1908,22850,1798],{},[1908,22852,11329],{},[1955,22854,3910],{},[1955,22856,1961],{"stretchy":1960},[1969,22858,1971],{},[1955,22860,3917],{},[1908,22862,1798],{},[2783,22864,22865,22867],{},[1955,22866,2023],{"stretchy":1960},[1908,22868,11329],{},[2783,22870,22871,22873],{},[1955,22872,2023],{"stretchy":1960},[1905,22874,22875,22877,22879],{},[1969,22876,1971],{},[1908,22878,11106],{"mathvariant":2789},[1908,22880,11329],{},[1912,22882,22883],{"encoding":1914},"w(p) = \\frac{p^\\gamma}{(p^\\gamma + (1-p)^\\gamma)^{1\u002F\\gamma}}",[1889,22885,22887,22914],{"className":22886,"ariaHidden":1919},[1918],[1889,22888,22890,22893,22896,22899,22902,22905,22908,22911],{"className":22889},[1923],[1889,22891],{"className":22892,"style":2057},[1927],[1889,22894,8472],{"className":22895,"style":8687},[1932,1933],[1889,22897,1961],{"className":22898},[2061],[1889,22900,1798],{"className":22901},[1932,1933],[1889,22903,2023],{"className":22904},[2367],[1889,22906],{"className":22907,"style":2043},[2042],[1889,22909,1957],{"className":22910},[2047],[1889,22912],{"className":22913,"style":2043},[2042],[1889,22915,22917,22921],{"className":22916},[1923],[1889,22918],{"className":22919,"style":22920},[1927],"height:2.2954em;vertical-align:-0.954em;",[1889,22922,22924,22927,23130],{"className":22923},[1932],[1889,22925],{"className":22926},[2061,6726],[1889,22928,22930],{"className":22929},[6567],[1889,22931,22933,23121],{"className":22932},[2075,2076],[1889,22934,22936,23118],{"className":22935},[2080],[1889,22937,22940,23073,23081],{"className":22938,"style":22939},[2084],"height:1.3414em;",[1889,22941,22943,22946],{"style":22942},"top:-2.296em;",[1889,22944],{"className":22945,"style":6746},[2092],[1889,22947,22949,22952,22981,22984,22987,22990,22993,22996,22999,23002,23005,23008,23037],{"className":22948},[1932],[1889,22950,1961],{"className":22951},[2061],[1889,22953,22955,22958],{"className":22954},[1932],[1889,22956,1798],{"className":22957},[1932,1933],[1889,22959,22961],{"className":22960},[2071],[1889,22962,22964],{"className":22963},[2075],[1889,22965,22967],{"className":22966},[2080],[1889,22968,22970],{"className":22969,"style":6768},[2084],[1889,22971,22972,22975],{"style":6771},[1889,22973],{"className":22974,"style":2093},[2092],[1889,22976,22978],{"className":22977},[2097,2098,2099,2100],[1889,22979,11329],{"className":22980,"style":11391},[1932,1933,2100],[1889,22982],{"className":22983,"style":4041},[2042],[1889,22985,3910],{"className":22986},[4045],[1889,22988],{"className":22989,"style":4041},[2042],[1889,22991,1961],{"className":22992},[2061],[1889,22994,1971],{"className":22995},[1932],[1889,22997],{"className":22998,"style":4041},[2042],[1889,23000,3917],{"className":23001},[4045],[1889,23003],{"className":23004,"style":4041},[2042],[1889,23006,1798],{"className":23007},[1932,1933],[1889,23009,23011,23014],{"className":23010},[2367],[1889,23012,2023],{"className":23013},[2367],[1889,23015,23017],{"className":23016},[2071],[1889,23018,23020],{"className":23019},[2075],[1889,23021,23023],{"className":23022},[2080],[1889,23024,23026],{"className":23025,"style":6768},[2084],[1889,23027,23028,23031],{"style":6771},[1889,23029],{"className":23030,"style":2093},[2092],[1889,23032,23034],{"className":23033},[2097,2098,2099,2100],[1889,23035,11329],{"className":23036,"style":11391},[1932,1933,2100],[1889,23038,23040,23043],{"className":23039},[2367],[1889,23041,2023],{"className":23042},[2367],[1889,23044,23046],{"className":23045},[2071],[1889,23047,23049],{"className":23048},[2075],[1889,23050,23052],{"className":23051},[2080],[1889,23053,23056],{"className":23054,"style":23055},[2084],"height:0.814em;",[1889,23057,23058,23061],{"style":6771},[1889,23059],{"className":23060,"style":2093},[2092],[1889,23062,23064],{"className":23063},[2097,2098,2099,2100],[1889,23065,23067,23070],{"className":23066},[1932,2100],[1889,23068,11124],{"className":23069},[1932,2100],[1889,23071,11329],{"className":23072,"style":11391},[1932,1933,2100],[1889,23074,23075,23078],{"style":6783},[1889,23076],{"className":23077,"style":6746},[2092],[1889,23079],{"className":23080,"style":6791},[6790],[1889,23082,23083,23086],{"style":6794},[1889,23084],{"className":23085,"style":6746},[2092],[1889,23087,23089],{"className":23088},[1932],[1889,23090,23092,23095],{"className":23091},[1932],[1889,23093,1798],{"className":23094},[1932,1933],[1889,23096,23098],{"className":23097},[2071],[1889,23099,23101],{"className":23100},[2075],[1889,23102,23104],{"className":23103},[2080],[1889,23105,23107],{"className":23106,"style":6489},[2084],[1889,23108,23109,23112],{"style":2825},[1889,23110],{"className":23111,"style":2093},[2092],[1889,23113,23115],{"className":23114},[2097,2098,2099,2100],[1889,23116,11329],{"className":23117,"style":11391},[1932,1933,2100],[1889,23119,2108],{"className":23120},[2107],[1889,23122,23124],{"className":23123},[2080],[1889,23125,23128],{"className":23126,"style":23127},[2084],"height:0.954em;",[1889,23129],{},[1889,23131],{"className":23132},[2367,6726],[22646,23134],{},[1889,23136,23138,23157],{"className":23137},[1892],[1889,23139,23141],{"className":23140},[1896],[1898,23142,23143],{"xmlns":1900},[1902,23144,23145,23154],{},[1905,23146,23147,23149,23151],{},[1908,23148,11329],{},[1955,23150,7183],{},[1969,23152,23153],{},"0.61",[1912,23155,23156],{"encoding":1914},"\\gamma \\approx 0.61",[1889,23158,23160,23179],{"className":23159,"ariaHidden":1919},[1918],[1889,23161,23163,23167,23170,23173,23176],{"className":23162},[1923],[1889,23164],{"className":23165,"style":23166},[1927],"height:0.6776em;vertical-align:-0.1944em;",[1889,23168,11329],{"className":23169,"style":11391},[1932,1933],[1889,23171],{"className":23172,"style":2043},[2042],[1889,23174,7183],{"className":23175},[2047],[1889,23177],{"className":23178,"style":2043},[2042],[1889,23180,23182,23185],{"className":23181},[1923],[1889,23183],{"className":23184,"style":2694},[1927],[1889,23186,23153],{"className":23187},[1932],[1808,23189,23190,23193],{},[1884,23191,23192],{},"参照点依赖",":\n效用取决于相对于某个参照点的变化，而非绝对水平。",[1877,23195,23197],{"id":23196},"_53-前景理论的预测","5.3 前景理论的预测",[1798,23199,23200,2704],{},[1884,23201,23202],{},"四重模式 (Fourfold Pattern)",[10841,23204,23205,23217],{},[10844,23206,23207],{},[10847,23208,23209,23211,23214],{},[10850,23210],{},[10850,23212,23213],{},"收益",[10850,23215,23216],{},"损失",[10994,23218,23219,23238],{},[10847,23220,23221,23226,23232],{},[10999,23222,23223],{},[1884,23224,23225],{},"高概率",[10999,23227,23228,23229,23231],{},"风险规避",[22646,23230],{},"（买保险）",[10999,23233,23234,23235,23237],{},"风险寻求",[22646,23236],{},"（赌博翻本）",[10847,23239,23240,23245,23250],{},[10999,23241,23242],{},[1884,23243,23244],{},"低概率",[10999,23246,23234,23247,23249],{},[22646,23248],{},"（买彩票）",[10999,23251,23228,23252,23231],{},[22646,23253],{},[1798,23255,23256],{},"这解释了为什么同一个人既买彩票（低概率高收益）又买保险（低概率高损失），而期望效用理论难以解释。",[1877,23258,23260],{"id":23259},"_54-禀赋效应与现状偏见","5.4 禀赋效应与现状偏见",[1798,23262,23263,23266],{},[1884,23264,23265],{},"禀赋效应 (Endowment Effect)",": 人们对自己拥有的东西赋予更高价值。",[1798,23268,23269,23272],{},[1884,23270,23271],{},"经典实验"," (Kahneman, Knetsch & Thaler, 1990):",[1805,23274,23275,23278,23281],{},[1808,23276,23277],{},"给一半学生一个咖啡杯",[1808,23279,23280],{},"询问拥有者的最低卖价（WTA）和非拥有者的最高买价（WTP）",[1808,23282,23283,23284],{},"发现",[1889,23285,23287,23319],{"className":23286},[1892],[1889,23288,23290],{"className":23289},[1896],[1898,23291,23292],{"xmlns":1900},[1902,23293,23294,23316],{},[1905,23295,23296,23299,23302,23304,23306,23308,23310,23312,23314],{},[1908,23297,23298],{},"W",[1908,23300,23301],{},"T",[1908,23303,9839],{},[1955,23305,7183],{},[1969,23307,1990],{},[1955,23309,16294],{},[1908,23311,23298],{},[1908,23313,23301],{},[1908,23315,9682],{},[1912,23317,23318],{"encoding":1914},"WTA \\approx 2 \\times WTP",[1889,23320,23322,23346,23364],{"className":23321,"ariaHidden":1919},[1918],[1889,23323,23325,23328,23331,23334,23337,23340,23343],{"className":23324},[1923],[1889,23326],{"className":23327,"style":1928},[1927],[1889,23329,23298],{"className":23330,"style":9722},[1932,1933],[1889,23332,23301],{"className":23333,"style":9722},[1932,1933],[1889,23335,9839],{"className":23336},[1932,1933],[1889,23338],{"className":23339,"style":2043},[2042],[1889,23341,7183],{"className":23342},[2047],[1889,23344],{"className":23345,"style":2043},[2042],[1889,23347,23349,23352,23355,23358,23361],{"className":23348},[1923],[1889,23350],{"className":23351,"style":12913},[1927],[1889,23353,1990],{"className":23354},[1932],[1889,23356],{"className":23357,"style":4041},[2042],[1889,23359,16294],{"className":23360},[4045],[1889,23362],{"className":23363,"style":4041},[2042],[1889,23365,23367,23370,23373,23376],{"className":23366},[1923],[1889,23368],{"className":23369,"style":1928},[1927],[1889,23371,23298],{"className":23372,"style":9722},[1932,1933],[1889,23374,23301],{"className":23375,"style":9722},[1932,1933],[1889,23377,9682],{"className":23378,"style":9722},[1932,1933],[1798,23380,23381,23382,23453],{},"期望效用理论预测",[1889,23383,23385,23411],{"className":23384},[1892],[1889,23386,23388],{"className":23387},[1896],[1898,23389,23390],{"xmlns":1900},[1902,23391,23392,23408],{},[1905,23393,23394,23396,23398,23400,23402,23404,23406],{},[1908,23395,23298],{},[1908,23397,23301],{},[1908,23399,9839],{},[1955,23401,1957],{},[1908,23403,23298],{},[1908,23405,23301],{},[1908,23407,9682],{},[1912,23409,23410],{"encoding":1914},"WTA = WTP",[1889,23412,23414,23438],{"className":23413,"ariaHidden":1919},[1918],[1889,23415,23417,23420,23423,23426,23429,23432,23435],{"className":23416},[1923],[1889,23418],{"className":23419,"style":1928},[1927],[1889,23421,23298],{"className":23422,"style":9722},[1932,1933],[1889,23424,23301],{"className":23425,"style":9722},[1932,1933],[1889,23427,9839],{"className":23428},[1932,1933],[1889,23430],{"className":23431,"style":2043},[2042],[1889,23433,1957],{"className":23434},[2047],[1889,23436],{"className":23437,"style":2043},[2042],[1889,23439,23441,23444,23447,23450],{"className":23440},[1923],[1889,23442],{"className":23443,"style":1928},[1927],[1889,23445,23298],{"className":23446,"style":9722},[1932,1933],[1889,23448,23301],{"className":23449,"style":9722},[1932,1933],[1889,23451,9682],{"className":23452,"style":9722},[1932,1933],"，但损失规避能解释这一差距。",[1870,23455],{},[1794,23457,23459],{"id":23458},"_6-完整例题","6. 完整例题",[1877,23461,23463],{"id":23462},"例题1-风险溢价的计算","例题1: 风险溢价的计算",[1798,23465,23466,23469,23470,23600,23601,23652],{},[1884,23467,23468],{},"题目",": 个体效用函数",[1889,23471,23473,23500],{"className":23472},[1892],[1889,23474,23476],{"className":23475},[1896],[1898,23477,23478],{"xmlns":1900},[1902,23479,23480,23497],{},[1905,23481,23482,23484,23486,23488,23490,23492],{},[1908,23483,5308],{},[1955,23485,1961],{"stretchy":1960},[1908,23487,8472],{},[1955,23489,2023],{"stretchy":1960},[1955,23491,1957],{},[23493,23494,23495],"msqrt",{},[1908,23496,8472],{},[1912,23498,23499],{"encoding":1914},"u(w) = \\sqrt{w}",[1889,23501,23503,23530],{"className":23502,"ariaHidden":1919},[1918],[1889,23504,23506,23509,23512,23515,23518,23521,23524,23527],{"className":23505},[1923],[1889,23507],{"className":23508,"style":2057},[1927],[1889,23510,5308],{"className":23511},[1932,1933],[1889,23513,1961],{"className":23514},[2061],[1889,23516,8472],{"className":23517,"style":8687},[1932,1933],[1889,23519,2023],{"className":23520},[2367],[1889,23522],{"className":23523,"style":2043},[2042],[1889,23525,1957],{"className":23526},[2047],[1889,23528],{"className":23529,"style":2043},[2042],[1889,23531,23533,23537],{"className":23532},[1923],[1889,23534],{"className":23535,"style":23536},[1927],"height:1.04em;vertical-align:-0.2397em;",[1889,23538,23541],{"className":23539},[1932,23540],"sqrt",[1889,23542,23544,23591],{"className":23543},[2075,2076],[1889,23545,23547,23588],{"className":23546},[2080],[1889,23548,23551,23565],{"className":23549,"style":23550},[2084],"height:0.8003em;",[1889,23552,23555,23558],{"className":23553,"style":8713},[23554],"svg-align",[1889,23556],{"className":23557,"style":6746},[2092],[1889,23559,23562],{"className":23560,"style":23561},[1932],"padding-left:0.833em;",[1889,23563,8472],{"className":23564,"style":8687},[1932,1933],[1889,23566,23568,23571],{"style":23567},"top:-2.7603em;",[1889,23569],{"className":23570,"style":6746},[2092],[1889,23572,23576],{"className":23573,"style":23575},[23574],"hide-tail","min-width:0.853em;height:1.08em;",[23577,23578,23584],"svg",{"xmlns":23579,"width":23580,"height":23581,"viewBox":23582,"preserveAspectRatio":23583},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[23585,23586],"path",{"d":23587},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[1889,23589,2108],{"className":23590},[2107],[1889,23592,23594],{"className":23593},[2080],[1889,23595,23598],{"className":23596,"style":23597},[2084],"height:0.2397em;",[1889,23599],{},"，当前财富",[1889,23602,23604,23622],{"className":23603},[1892],[1889,23605,23607],{"className":23606},[1896],[1898,23608,23609],{"xmlns":1900},[1902,23610,23611,23619],{},[1905,23612,23613,23615,23617],{},[1908,23614,8472],{},[1955,23616,1957],{},[1969,23618,16040],{},[1912,23620,23621],{"encoding":1914},"w = 100",[1889,23623,23625,23643],{"className":23624,"ariaHidden":1919},[1918],[1889,23626,23628,23631,23634,23637,23640],{"className":23627},[1923],[1889,23629],{"className":23630,"style":5332},[1927],[1889,23632,8472],{"className":23633,"style":8687},[1932,1933],[1889,23635],{"className":23636,"style":2043},[2042],[1889,23638,1957],{"className":23639},[2047],[1889,23641],{"className":23642,"style":2043},[2042],[1889,23644,23646,23649],{"className":23645},[1923],[1889,23647],{"className":23648,"style":2694},[1927],[1889,23650,16040],{"className":23651},[1932],"。面临赌博：50%概率赢36，50%概率输36。求风险溢价。",[1798,23654,23655,2704],{},[1884,23656,23657],{},"解答",[1798,23659,23660,23661],{},"期望财富：",[1889,23662,23664,23721],{"className":23663},[1892],[1889,23665,23667],{"className":23666},[1896],[1898,23668,23669],{"xmlns":1900},[1902,23670,23671,23718],{},[1905,23672,23673,23675,23677,23683,23685,23687,23690,23692,23694,23696,23698,23700,23702,23704,23706,23708,23710,23712,23714,23716],{},[1908,23674,5719],{"mathvariant":5313},[1955,23676,5722],{"stretchy":1960},[8476,23678,23679,23681],{"accent":1919},[1908,23680,8472],{},[1955,23682,8483],{},[1955,23684,5733],{"stretchy":1960},[1955,23686,1957],{},[1969,23688,23689],{},"0.5",[1955,23691,1961],{"stretchy":1960},[1969,23693,16040],{},[1955,23695,3910],{},[1969,23697,16129],{},[1955,23699,2023],{"stretchy":1960},[1955,23701,3910],{},[1969,23703,23689],{},[1955,23705,1961],{"stretchy":1960},[1969,23707,16040],{},[1955,23709,3917],{},[1969,23711,16129],{},[1955,23713,2023],{"stretchy":1960},[1955,23715,1957],{},[1969,23717,16040],{},[1912,23719,23720],{"encoding":1914},"\\mathbb{E}[\\tilde{w}] = 0.5(100+36) + 0.5(100-36) = 100",[1889,23722,23724,23779,23803,23824,23848,23869],{"className":23723,"ariaHidden":1919},[1918],[1889,23725,23727,23730,23733,23736,23767,23770,23773,23776],{"className":23726},[1923],[1889,23728],{"className":23729,"style":2057},[1927],[1889,23731,5719],{"className":23732},[1932,5355],[1889,23734,5722],{"className":23735},[2061],[1889,23737,23739],{"className":23738},[1932,8700],[1889,23740,23742],{"className":23741},[2075],[1889,23743,23745],{"className":23744},[2080],[1889,23746,23748,23756],{"className":23747,"style":8710},[2084],[1889,23749,23750,23753],{"style":8713},[1889,23751],{"className":23752,"style":6746},[2092],[1889,23754,8472],{"className":23755,"style":8687},[1932,1933],[1889,23757,23758,23761],{"style":8722},[1889,23759],{"className":23760,"style":6746},[2092],[1889,23762,23764],{"className":23763,"style":9650},[8729],[1889,23765,8483],{"className":23766},[1932],[1889,23768,5733],{"className":23769},[2367],[1889,23771],{"className":23772,"style":2043},[2042],[1889,23774,1957],{"className":23775},[2047],[1889,23777],{"className":23778,"style":2043},[2042],[1889,23780,23782,23785,23788,23791,23794,23797,23800],{"className":23781},[1923],[1889,23783],{"className":23784,"style":2057},[1927],[1889,23786,23689],{"className":23787},[1932],[1889,23789,1961],{"className":23790},[2061],[1889,23792,16040],{"className":23793},[1932],[1889,23795],{"className":23796,"style":4041},[2042],[1889,23798,3910],{"className":23799},[4045],[1889,23801],{"className":23802,"style":4041},[2042],[1889,23804,23806,23809,23812,23815,23818,23821],{"className":23805},[1923],[1889,23807],{"className":23808,"style":2057},[1927],[1889,23810,16129],{"className":23811},[1932],[1889,23813,2023],{"className":23814},[2367],[1889,23816],{"className":23817,"style":4041},[2042],[1889,23819,3910],{"className":23820},[4045],[1889,23822],{"className":23823,"style":4041},[2042],[1889,23825,23827,23830,23833,23836,23839,23842,23845],{"className":23826},[1923],[1889,23828],{"className":23829,"style":2057},[1927],[1889,23831,23689],{"className":23832},[1932],[1889,23834,1961],{"className":23835},[2061],[1889,23837,16040],{"className":23838},[1932],[1889,23840],{"className":23841,"style":4041},[2042],[1889,23843,3917],{"className":23844},[4045],[1889,23846],{"className":23847,"style":4041},[2042],[1889,23849,23851,23854,23857,23860,23863,23866],{"className":23850},[1923],[1889,23852],{"className":23853,"style":2057},[1927],[1889,23855,16129],{"className":23856},[1932],[1889,23858,2023],{"className":23859},[2367],[1889,23861],{"className":23862,"style":2043},[2042],[1889,23864,1957],{"className":23865},[2047],[1889,23867],{"className":23868,"style":2043},[2042],[1889,23870,23872,23875],{"className":23871},[1923],[1889,23873],{"className":23874,"style":2694},[1927],[1889,23876,16040],{"className":23877},[1932],[1798,23879,23880,23881],{},"期望效用：",[1889,23882,23884,23958],{"className":23883},[1892],[1889,23885,23887],{"className":23886},[1896],[1898,23888,23889],{"xmlns":1900},[1902,23890,23891,23955],{},[1905,23892,23893,23895,23897,23899,23901,23907,23909,23911,23913,23915,23920,23922,23924,23928,23930,23932,23934,23937,23939,23941,23943,23945,23948,23950,23952],{},[1908,23894,5719],{"mathvariant":5313},[1955,23896,5722],{"stretchy":1960},[1908,23898,5308],{},[1955,23900,1961],{"stretchy":1960},[8476,23902,23903,23905],{"accent":1919},[1908,23904,8472],{},[1955,23906,8483],{},[1955,23908,2023],{"stretchy":1960},[1955,23910,5733],{"stretchy":1960},[1955,23912,1957],{},[1969,23914,23689],{},[23493,23916,23917],{},[1969,23918,23919],{},"136",[1955,23921,3910],{},[1969,23923,23689],{},[23493,23925,23926],{},[1969,23927,16324],{},[1955,23929,1957],{},[1969,23931,23689],{},[1955,23933,1961],{"stretchy":1960},[1969,23935,23936],{},"11.66",[1955,23938,2023],{"stretchy":1960},[1955,23940,3910],{},[1969,23942,23689],{},[1955,23944,1961],{"stretchy":1960},[1969,23946,23947],{},"8",[1955,23949,2023],{"stretchy":1960},[1955,23951,1957],{},[1969,23953,23954],{},"9.83",[1912,23956,23957],{"encoding":1914},"\\mathbb{E}[u(\\tilde{w})] = 0.5\\sqrt{136} + 0.5\\sqrt{64} = 0.5(11.66) + 0.5(8) = 9.83",[1889,23959,23961,24022,24091,24156,24183,24210],{"className":23960,"ariaHidden":1919},[1918],[1889,23962,23964,23967,23970,23973,23976,23979,24010,24013,24016,24019],{"className":23963},[1923],[1889,23965],{"className":23966,"style":2057},[1927],[1889,23968,5719],{"className":23969},[1932,5355],[1889,23971,5722],{"className":23972},[2061],[1889,23974,5308],{"className":23975},[1932,1933],[1889,23977,1961],{"className":23978},[2061],[1889,23980,23982],{"className":23981},[1932,8700],[1889,23983,23985],{"className":23984},[2075],[1889,23986,23988],{"className":23987},[2080],[1889,23989,23991,23999],{"className":23990,"style":8710},[2084],[1889,23992,23993,23996],{"style":8713},[1889,23994],{"className":23995,"style":6746},[2092],[1889,23997,8472],{"className":23998,"style":8687},[1932,1933],[1889,24000,24001,24004],{"style":8722},[1889,24002],{"className":24003,"style":6746},[2092],[1889,24005,24007],{"className":24006,"style":9650},[8729],[1889,24008,8483],{"className":24009},[1932],[1889,24011,5972],{"className":24012},[2367],[1889,24014],{"className":24015,"style":2043},[2042],[1889,24017,1957],{"className":24018},[2047],[1889,24020],{"className":24021,"style":2043},[2042],[1889,24023,24025,24029,24032,24082,24085,24088],{"className":24024},[1923],[1889,24026],{"className":24027,"style":24028},[1927],"height:1.04em;vertical-align:-0.1328em;",[1889,24030,23689],{"className":24031},[1932],[1889,24033,24035],{"className":24034},[1932,23540],[1889,24036,24038,24073],{"className":24037},[2075,2076],[1889,24039,24041,24070],{"className":24040},[2080],[1889,24042,24045,24057],{"className":24043,"style":24044},[2084],"height:0.9072em;",[1889,24046,24048,24051],{"className":24047,"style":8713},[23554],[1889,24049],{"className":24050,"style":6746},[2092],[1889,24052,24054],{"className":24053,"style":23561},[1932],[1889,24055,23919],{"className":24056},[1932],[1889,24058,24060,24063],{"style":24059},"top:-2.8672em;",[1889,24061],{"className":24062,"style":6746},[2092],[1889,24064,24066],{"className":24065,"style":23575},[23574],[23577,24067,24068],{"xmlns":23579,"width":23580,"height":23581,"viewBox":23582,"preserveAspectRatio":23583},[23585,24069],{"d":23587},[1889,24071,2108],{"className":24072},[2107],[1889,24074,24076],{"className":24075},[2080],[1889,24077,24080],{"className":24078,"style":24079},[2084],"height:0.1328em;",[1889,24081],{},[1889,24083],{"className":24084,"style":4041},[2042],[1889,24086,3910],{"className":24087},[4045],[1889,24089],{"className":24090,"style":4041},[2042],[1889,24092,24094,24097,24100,24147,24150,24153],{"className":24093},[1923],[1889,24095],{"className":24096,"style":24028},[1927],[1889,24098,23689],{"className":24099},[1932],[1889,24101,24103],{"className":24102},[1932,23540],[1889,24104,24106,24139],{"className":24105},[2075,2076],[1889,24107,24109,24136],{"className":24108},[2080],[1889,24110,24112,24124],{"className":24111,"style":24044},[2084],[1889,24113,24115,24118],{"className":24114,"style":8713},[23554],[1889,24116],{"className":24117,"style":6746},[2092],[1889,24119,24121],{"className":24120,"style":23561},[1932],[1889,24122,16324],{"className":24123},[1932],[1889,24125,24126,24129],{"style":24059},[1889,24127],{"className":24128,"style":6746},[2092],[1889,24130,24132],{"className":24131,"style":23575},[23574],[23577,24133,24134],{"xmlns":23579,"width":23580,"height":23581,"viewBox":23582,"preserveAspectRatio":23583},[23585,24135],{"d":23587},[1889,24137,2108],{"className":24138},[2107],[1889,24140,24142],{"className":24141},[2080],[1889,24143,24145],{"className":24144,"style":24079},[2084],[1889,24146],{},[1889,24148],{"className":24149,"style":2043},[2042],[1889,24151,1957],{"className":24152},[2047],[1889,24154],{"className":24155,"style":2043},[2042],[1889,24157,24159,24162,24165,24168,24171,24174,24177,24180],{"className":24158},[1923],[1889,24160],{"className":24161,"style":2057},[1927],[1889,24163,23689],{"className":24164},[1932],[1889,24166,1961],{"className":24167},[2061],[1889,24169,23936],{"className":24170},[1932],[1889,24172,2023],{"className":24173},[2367],[1889,24175],{"className":24176,"style":4041},[2042],[1889,24178,3910],{"className":24179},[4045],[1889,24181],{"className":24182,"style":4041},[2042],[1889,24184,24186,24189,24192,24195,24198,24201,24204,24207],{"className":24185},[1923],[1889,24187],{"className":24188,"style":2057},[1927],[1889,24190,23689],{"className":24191},[1932],[1889,24193,1961],{"className":24194},[2061],[1889,24196,23947],{"className":24197},[1932],[1889,24199,2023],{"className":24200},[2367],[1889,24202],{"className":24203,"style":2043},[2042],[1889,24205,1957],{"className":24206},[2047],[1889,24208],{"className":24209,"style":2043},[2042],[1889,24211,24213,24216],{"className":24212},[1923],[1889,24214],{"className":24215,"style":2694},[1927],[1889,24217,23954],{"className":24218},[1932],[1798,24220,24221,24222],{},"确定性等价：",[1889,24223,24225,24284],{"className":24224},[1892],[1889,24226,24228],{"className":24227},[1896],[1898,24229,24230],{"xmlns":1900},[1902,24231,24232,24281],{},[1905,24233,24234,24236,24238,24240,24242,24244,24246,24248,24250,24252,24254,24262,24264,24266,24268,24270,24272,24274,24276,24278],{},[1908,24235,5308],{},[1955,24237,1961],{"stretchy":1960},[1908,24239,9541],{},[1908,24241,5719],{},[1955,24243,2023],{"stretchy":1960},[1955,24245,1957],{},[1969,24247,23954],{},[2960,24249,13957],{},[1955,24251,13960],{},[2960,24253,13957],{},[23493,24255,24256],{},[1905,24257,24258,24260],{},[1908,24259,9541],{},[1908,24261,5719],{},[1955,24263,1957],{},[1969,24265,23954],{},[2960,24267,13957],{},[1955,24269,13960],{},[2960,24271,13957],{},[1908,24273,9541],{},[1908,24275,5719],{},[1955,24277,1957],{},[1969,24279,24280],{},"96.63",[1912,24282,24283],{"encoding":1914},"u(CE) = 9.83 \\implies \\sqrt{CE} = 9.83 \\implies CE = 96.63",[1889,24285,24287,24317,24342,24411,24435,24456],{"className":24286,"ariaHidden":1919},[1918],[1889,24288,24290,24293,24296,24299,24302,24305,24308,24311,24314],{"className":24289},[1923],[1889,24291],{"className":24292,"style":2057},[1927],[1889,24294,5308],{"className":24295},[1932,1933],[1889,24297,1961],{"className":24298},[2061],[1889,24300,9541],{"className":24301,"style":9587},[1932,1933],[1889,24303,5719],{"className":24304,"style":9591},[1932,1933],[1889,24306,2023],{"className":24307},[2367],[1889,24309],{"className":24310,"style":2043},[2042],[1889,24312,1957],{"className":24313},[2047],[1889,24315],{"className":24316,"style":2043},[2042],[1889,24318,24320,24324,24327,24330,24333,24336,24339],{"className":24319},[1923],[1889,24321],{"className":24322,"style":24323},[1927],"height:0.6684em;vertical-align:-0.024em;",[1889,24325,23954],{"className":24326},[1932],[1889,24328],{"className":24329,"style":2043},[2042],[1889,24331],{"className":24332,"style":2043},[2042],[1889,24334,13960],{"className":24335},[2047],[1889,24337],{"className":24338,"style":2043},[2042],[1889,24340],{"className":24341,"style":2043},[2042],[1889,24343,24345,24349,24402,24405,24408],{"className":24344},[1923],[1889,24346],{"className":24347,"style":24348},[1927],"height:1.04em;vertical-align:-0.1133em;",[1889,24350,24352],{"className":24351},[1932,23540],[1889,24353,24355,24393],{"className":24354},[2075,2076],[1889,24356,24358,24390],{"className":24357},[2080],[1889,24359,24362,24377],{"className":24360,"style":24361},[2084],"height:0.9267em;",[1889,24363,24365,24368],{"className":24364,"style":8713},[23554],[1889,24366],{"className":24367,"style":6746},[2092],[1889,24369,24371,24374],{"className":24370,"style":23561},[1932],[1889,24372,9541],{"className":24373,"style":9587},[1932,1933],[1889,24375,5719],{"className":24376,"style":9591},[1932,1933],[1889,24378,24380,24383],{"style":24379},"top:-2.8867em;",[1889,24381],{"className":24382,"style":6746},[2092],[1889,24384,24386],{"className":24385,"style":23575},[23574],[23577,24387,24388],{"xmlns":23579,"width":23580,"height":23581,"viewBox":23582,"preserveAspectRatio":23583},[23585,24389],{"d":23587},[1889,24391,2108],{"className":24392},[2107],[1889,24394,24396],{"className":24395},[2080],[1889,24397,24400],{"className":24398,"style":24399},[2084],"height:0.1133em;",[1889,24401],{},[1889,24403],{"className":24404,"style":2043},[2042],[1889,24406,1957],{"className":24407},[2047],[1889,24409],{"className":24410,"style":2043},[2042],[1889,24412,24414,24417,24420,24423,24426,24429,24432],{"className":24413},[1923],[1889,24415],{"className":24416,"style":24323},[1927],[1889,24418,23954],{"className":24419},[1932],[1889,24421],{"className":24422,"style":2043},[2042],[1889,24424],{"className":24425,"style":2043},[2042],[1889,24427,13960],{"className":24428},[2047],[1889,24430],{"className":24431,"style":2043},[2042],[1889,24433],{"className":24434,"style":2043},[2042],[1889,24436,24438,24441,24444,24447,24450,24453],{"className":24437},[1923],[1889,24439],{"className":24440,"style":1928},[1927],[1889,24442,9541],{"className":24443,"style":9587},[1932,1933],[1889,24445,5719],{"className":24446,"style":9591},[1932,1933],[1889,24448],{"className":24449,"style":2043},[2042],[1889,24451,1957],{"className":24452},[2047],[1889,24454],{"className":24455,"style":2043},[2042],[1889,24457,24459,24462],{"className":24458},[1923],[1889,24460],{"className":24461,"style":2694},[1927],[1889,24463,24280],{"className":24464},[1932],[1798,24466,24467,24468],{},"风险溢价：",[1889,24469,24471,24500],{"className":24470},[1892],[1889,24472,24474],{"className":24473},[1896],[1898,24475,24476],{"xmlns":1900},[1902,24477,24478,24497],{},[1905,24479,24480,24482,24484,24486,24488,24490,24492,24494],{},[1908,24481,5314],{},[1908,24483,9682],{},[1955,24485,1957],{},[1969,24487,16040],{},[1955,24489,3917],{},[1969,24491,24280],{},[1955,24493,1957],{},[1969,24495,24496],{},"3.37",[1912,24498,24499],{"encoding":1914},"RP = 100 - 96.63 = 3.37",[1889,24501,24503,24524,24542,24560],{"className":24502,"ariaHidden":1919},[1918],[1889,24504,24506,24509,24512,24515,24518,24521],{"className":24505},[1923],[1889,24507],{"className":24508,"style":1928},[1927],[1889,24510,5314],{"className":24511,"style":9718},[1932,1933],[1889,24513,9682],{"className":24514,"style":9722},[1932,1933],[1889,24516],{"className":24517,"style":2043},[2042],[1889,24519,1957],{"className":24520},[2047],[1889,24522],{"className":24523,"style":2043},[2042],[1889,24525,24527,24530,24533,24536,24539],{"className":24526},[1923],[1889,24528],{"className":24529,"style":12913},[1927],[1889,24531,16040],{"className":24532},[1932],[1889,24534],{"className":24535,"style":4041},[2042],[1889,24537,3917],{"className":24538},[4045],[1889,24540],{"className":24541,"style":4041},[2042],[1889,24543,24545,24548,24551,24554,24557],{"className":24544},[1923],[1889,24546],{"className":24547,"style":2694},[1927],[1889,24549,24280],{"className":24550},[1932],[1889,24552],{"className":24553,"style":2043},[2042],[1889,24555,1957],{"className":24556},[2047],[1889,24558],{"className":24559,"style":2043},[2042],[1889,24561,24563,24566],{"className":24562},[1923],[1889,24564],{"className":24565,"style":2694},[1927],[1889,24567,24496],{"className":24568},[1932],[1798,24570,24571,24574],{},[1884,24572,24573],{},"解释",": 该个体愿意放弃3.37元来避免这个公平赌博。",[1798,24576,24577,24580],{},[1884,24578,24579],{},"验证",": 使用近似公式",[1889,24582,24584],{"className":24583},[1938],[1889,24585,24587,24719],{"className":24586},[1892],[1889,24588,24590],{"className":24589},[1896],[1898,24591,24592],{"xmlns":1900,"display":1947},[1902,24593,24594,24716],{},[1905,24595,24596,24598,24600,24602,24604,24606,24608,24642,24644,24646,24695,24697,24707,24709],{},[1908,24597,9839],{},[1955,24599,1961],{"stretchy":1960},[1908,24601,8472],{},[1955,24603,2023],{"stretchy":1960},[1955,24605,1957],{},[1955,24607,3917],{},[6567,24609,24610,24628],{},[1905,24611,24612,24622,24624,24626],{},[2783,24613,24614,24616],{},[1908,24615,5308],{},[1905,24617,24618,24620],{},[1955,24619,2791],{"mathvariant":2789},[1955,24621,2791],{"mathvariant":2789},[1955,24623,1961],{"stretchy":1960},[1908,24625,8472],{},[1955,24627,2023],{"stretchy":1960},[1905,24629,24630,24636,24638,24640],{},[2783,24631,24632,24634],{},[1908,24633,5308],{},[1955,24635,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,24637,1961],{"stretchy":1960},[1908,24639,8472],{},[1955,24641,2023],{"stretchy":1960},[1955,24643,1957],{},[1955,24645,3917],{},[6567,24647,24648,24673],{},[1905,24649,24650,24652,24659],{},[1955,24651,3917],{},[6567,24653,24654,24656],{},[1969,24655,1971],{},[1969,24657,24658],{},"4",[2783,24660,24661,24663],{},[1908,24662,8472],{},[1905,24664,24665,24667,24669,24671],{},[1955,24666,3917],{},[1969,24668,3352],{},[1908,24670,11106],{"mathvariant":2789},[1969,24672,1990],{},[1905,24674,24675,24681],{},[6567,24676,24677,24679],{},[1969,24678,1971],{},[1969,24680,1990],{},[2783,24682,24683,24685],{},[1908,24684,8472],{},[1905,24686,24687,24689,24691,24693],{},[1955,24688,3917],{},[1969,24690,1971],{},[1908,24692,11106],{"mathvariant":2789},[1969,24694,1990],{},[1955,24696,1957],{},[6567,24698,24699,24701],{},[1969,24700,1971],{},[1905,24702,24703,24705],{},[1969,24704,1990],{},[1908,24706,8472],{},[1955,24708,1957],{},[6567,24710,24711,24713],{},[1969,24712,1971],{},[1969,24714,24715],{},"200",[1912,24717,24718],{"encoding":1914},"A(w) = -\\frac{u''(w)}{u'(w)} = -\\frac{-\\frac{1}{4}w^{-3\u002F2}}{\\frac{1}{2}w^{-1\u002F2}} = \\frac{1}{2w} = \\frac{1}{200}",[1889,24720,24722,24749,24905,25197,25277],{"className":24721,"ariaHidden":1919},[1918],[1889,24723,24725,24728,24731,24734,24737,24740,24743,24746],{"className":24724},[1923],[1889,24726],{"className":24727,"style":2057},[1927],[1889,24729,9839],{"className":24730},[1932,1933],[1889,24732,1961],{"className":24733},[2061],[1889,24735,8472],{"className":24736,"style":8687},[1932,1933],[1889,24738,2023],{"className":24739},[2367],[1889,24741],{"className":24742,"style":2043},[2042],[1889,24744,1957],{"className":24745},[2047],[1889,24747],{"className":24748,"style":2043},[2042],[1889,24750,24752,24755,24758,24896,24899,24902],{"className":24751},[1923],[1889,24753],{"className":24754,"style":9923},[1927],[1889,24756,3917],{"className":24757},[1932],[1889,24759,24761,24764,24893],{"className":24760},[1932],[1889,24762],{"className":24763},[2061,6726],[1889,24765,24767],{"className":24766},[6567],[1889,24768,24770,24885],{"className":24769},[2075,2076],[1889,24771,24773,24882],{"className":24772},[2080],[1889,24774,24776,24825,24833],{"className":24775,"style":9945},[2084],[1889,24777,24778,24781],{"style":6742},[1889,24779],{"className":24780,"style":6746},[2092],[1889,24782,24784,24816,24819,24822],{"className":24783},[1932],[1889,24785,24787,24790],{"className":24786},[1932],[1889,24788,5308],{"className":24789},[1932,1933],[1889,24791,24793],{"className":24792},[2071],[1889,24794,24796],{"className":24795},[2075],[1889,24797,24799],{"className":24798},[2080],[1889,24800,24802],{"className":24801,"style":9972},[2084],[1889,24803,24804,24807],{"style":6771},[1889,24805],{"className":24806,"style":2093},[2092],[1889,24808,24810],{"className":24809},[2097,2098,2099,2100],[1889,24811,24813],{"className":24812},[1932,2100],[1889,24814,2791],{"className":24815},[1932,2100],[1889,24817,1961],{"className":24818},[2061],[1889,24820,8472],{"className":24821,"style":8687},[1932,1933],[1889,24823,2023],{"className":24824},[2367],[1889,24826,24827,24830],{"style":6783},[1889,24828],{"className":24829,"style":6746},[2092],[1889,24831],{"className":24832,"style":6791},[6790],[1889,24834,24835,24838],{"style":6794},[1889,24836],{"className":24837,"style":6746},[2092],[1889,24839,24841,24873,24876,24879],{"className":24840},[1932],[1889,24842,24844,24847],{"className":24843},[1932],[1889,24845,5308],{"className":24846},[1932,1933],[1889,24848,24850],{"className":24849},[2071],[1889,24851,24853],{"className":24852},[2075],[1889,24854,24856],{"className":24855},[2080],[1889,24857,24859],{"className":24858,"style":2804},[2084],[1889,24860,24861,24864],{"style":2825},[1889,24862],{"className":24863,"style":2093},[2092],[1889,24865,24867],{"className":24866},[2097,2098,2099,2100],[1889,24868,24870],{"className":24869},[1932,2100],[1889,24871,8176],{"className":24872},[1932,2100],[1889,24874,1961],{"className":24875},[2061],[1889,24877,8472],{"className":24878,"style":8687},[1932,1933],[1889,24880,2023],{"className":24881},[2367],[1889,24883,2108],{"className":24884},[2107],[1889,24886,24888],{"className":24887},[2080],[1889,24889,24891],{"className":24890,"style":10062},[2084],[1889,24892],{},[1889,24894],{"className":24895},[2367,6726],[1889,24897],{"className":24898,"style":2043},[2042],[1889,24900,1957],{"className":24901},[2047],[1889,24903],{"className":24904,"style":2043},[2042],[1889,24906,24908,24912,24915,25188,25191,25194],{"className":24907},[1923],[1889,24909],{"className":24910,"style":24911},[1927],"height:2.7031em;vertical-align:-1.0801em;",[1889,24913,3917],{"className":24914},[1932],[1889,24916,24918,24921,25185],{"className":24917},[1932],[1889,24919],{"className":24920},[2061,6726],[1889,24922,24924],{"className":24923},[6567],[1889,24925,24927,25176],{"className":24926},[2075,2076],[1889,24928,24930,25173],{"className":24929},[2080],[1889,24931,24934,25048,25056],{"className":24932,"style":24933},[2084],"height:1.623em;",[1889,24935,24937,24940],{"style":24936},"top:-2.2649em;",[1889,24938],{"className":24939,"style":6746},[2092],[1889,24941,24943,25012],{"className":24942},[1932],[1889,24944,24946,24949,25009],{"className":24945},[1932],[1889,24947],{"className":24948},[2061,6726],[1889,24950,24952],{"className":24951},[6567],[1889,24953,24955,25001],{"className":24954},[2075,2076],[1889,24956,24958,24998],{"className":24957},[2080],[1889,24959,24962,24976,24984],{"className":24960,"style":24961},[2084],"height:0.8451em;",[1889,24963,24964,24967],{"style":11372},[1889,24965],{"className":24966,"style":6746},[2092],[1889,24968,24970],{"className":24969},[2097,2098,2099,2100],[1889,24971,24973],{"className":24972},[1932,2100],[1889,24974,1990],{"className":24975},[1932,2100],[1889,24977,24978,24981],{"style":6783},[1889,24979],{"className":24980,"style":6746},[2092],[1889,24982],{"className":24983,"style":6791},[6790],[1889,24985,24986,24989],{"style":11402},[1889,24987],{"className":24988,"style":6746},[2092],[1889,24990,24992],{"className":24991},[2097,2098,2099,2100],[1889,24993,24995],{"className":24994},[1932,2100],[1889,24996,1971],{"className":24997},[1932,2100],[1889,24999,2108],{"className":25000},[2107],[1889,25002,25004],{"className":25003},[2080],[1889,25005,25007],{"className":25006,"style":11676},[2084],[1889,25008],{},[1889,25010],{"className":25011},[2367,6726],[1889,25013,25015,25018],{"className":25014},[1932],[1889,25016,8472],{"className":25017,"style":8687},[1932,1933],[1889,25019,25021],{"className":25020},[2071],[1889,25022,25024],{"className":25023},[2075],[1889,25025,25027],{"className":25026},[2080],[1889,25028,25030],{"className":25029,"style":23055},[2084],[1889,25031,25032,25035],{"style":6771},[1889,25033],{"className":25034,"style":2093},[2092],[1889,25036,25038],{"className":25037},[2097,2098,2099,2100],[1889,25039,25041,25044],{"className":25040},[1932,2100],[1889,25042,3917],{"className":25043},[1932,2100],[1889,25045,25047],{"className":25046},[1932,2100],"1\u002F2",[1889,25049,25050,25053],{"style":6783},[1889,25051],{"className":25052,"style":6746},[2092],[1889,25054],{"className":25055,"style":6791},[6790],[1889,25057,25059,25062],{"style":25058},"top:-3.735em;",[1889,25060],{"className":25061,"style":6746},[2092],[1889,25063,25065,25068,25136],{"className":25064},[1932],[1889,25066,3917],{"className":25067},[1932],[1889,25069,25071,25074,25133],{"className":25070},[1932],[1889,25072],{"className":25073},[2061,6726],[1889,25075,25077],{"className":25076},[6567],[1889,25078,25080,25125],{"className":25079},[2075,2076],[1889,25081,25083,25122],{"className":25082},[2080],[1889,25084,25086,25100,25108],{"className":25085,"style":24961},[2084],[1889,25087,25088,25091],{"style":11372},[1889,25089],{"className":25090,"style":6746},[2092],[1889,25092,25094],{"className":25093},[2097,2098,2099,2100],[1889,25095,25097],{"className":25096},[1932,2100],[1889,25098,24658],{"className":25099},[1932,2100],[1889,25101,25102,25105],{"style":6783},[1889,25103],{"className":25104,"style":6746},[2092],[1889,25106],{"className":25107,"style":6791},[6790],[1889,25109,25110,25113],{"style":11402},[1889,25111],{"className":25112,"style":6746},[2092],[1889,25114,25116],{"className":25115},[2097,2098,2099,2100],[1889,25117,25119],{"className":25118},[1932,2100],[1889,25120,1971],{"className":25121},[1932,2100],[1889,25123,2108],{"className":25124},[2107],[1889,25126,25128],{"className":25127},[2080],[1889,25129,25131],{"className":25130,"style":11676},[2084],[1889,25132],{},[1889,25134],{"className":25135},[2367,6726],[1889,25137,25139,25142],{"className":25138},[1932],[1889,25140,8472],{"className":25141,"style":8687},[1932,1933],[1889,25143,25145],{"className":25144},[2071],[1889,25146,25148],{"className":25147},[2075],[1889,25149,25151],{"className":25150},[2080],[1889,25152,25155],{"className":25153,"style":25154},[2084],"height:0.888em;",[1889,25156,25157,25160],{"style":2825},[1889,25158],{"className":25159,"style":2093},[2092],[1889,25161,25163],{"className":25162},[2097,2098,2099,2100],[1889,25164,25166,25169],{"className":25165},[1932,2100],[1889,25167,3917],{"className":25168},[1932,2100],[1889,25170,25172],{"className":25171},[1932,2100],"3\u002F2",[1889,25174,2108],{"className":25175},[2107],[1889,25177,25179],{"className":25178},[2080],[1889,25180,25183],{"className":25181,"style":25182},[2084],"height:1.0801em;",[1889,25184],{},[1889,25186],{"className":25187},[2367,6726],[1889,25189],{"className":25190,"style":2043},[2042],[1889,25192,1957],{"className":25193},[2047],[1889,25195],{"className":25196,"style":2043},[2042],[1889,25198,25200,25203,25268,25271,25274],{"className":25199},[1923],[1889,25201],{"className":25202,"style":10595},[1927],[1889,25204,25206,25209,25265],{"className":25205},[1932],[1889,25207],{"className":25208},[2061,6726],[1889,25210,25212],{"className":25211},[6567],[1889,25213,25215,25257],{"className":25214},[2075,2076],[1889,25216,25218,25254],{"className":25217},[2080],[1889,25219,25221,25235,25243],{"className":25220,"style":6739},[2084],[1889,25222,25223,25226],{"style":6742},[1889,25224],{"className":25225,"style":6746},[2092],[1889,25227,25229,25232],{"className":25228},[1932],[1889,25230,1990],{"className":25231},[1932],[1889,25233,8472],{"className":25234,"style":8687},[1932,1933],[1889,25236,25237,25240],{"style":6783},[1889,25238],{"className":25239,"style":6746},[2092],[1889,25241],{"className":25242,"style":6791},[6790],[1889,25244,25245,25248],{"style":6794},[1889,25246],{"className":25247,"style":6746},[2092],[1889,25249,25251],{"className":25250},[1932],[1889,25252,1971],{"className":25253},[1932],[1889,25255,2108],{"className":25256},[2107],[1889,25258,25260],{"className":25259},[2080],[1889,25261,25263],{"className":25262,"style":6813},[2084],[1889,25264],{},[1889,25266],{"className":25267},[2367,6726],[1889,25269],{"className":25270,"style":2043},[2042],[1889,25272,1957],{"className":25273},[2047],[1889,25275],{"className":25276,"style":2043},[2042],[1889,25278,25280,25283],{"className":25279},[1923],[1889,25281],{"className":25282,"style":10595},[1927],[1889,25284,25286,25289,25342],{"className":25285},[1932],[1889,25287],{"className":25288},[2061,6726],[1889,25290,25292],{"className":25291},[6567],[1889,25293,25295,25334],{"className":25294},[2075,2076],[1889,25296,25298,25331],{"className":25297},[2080],[1889,25299,25301,25312,25320],{"className":25300,"style":6739},[2084],[1889,25302,25303,25306],{"style":6742},[1889,25304],{"className":25305,"style":6746},[2092],[1889,25307,25309],{"className":25308},[1932],[1889,25310,24715],{"className":25311},[1932],[1889,25313,25314,25317],{"style":6783},[1889,25315],{"className":25316,"style":6746},[2092],[1889,25318],{"className":25319,"style":6791},[6790],[1889,25321,25322,25325],{"style":6794},[1889,25323],{"className":25324,"style":6746},[2092],[1889,25326,25328],{"className":25327},[1932],[1889,25329,1971],{"className":25330},[1932],[1889,25332,2108],{"className":25333},[2107],[1889,25335,25337],{"className":25336},[2080],[1889,25338,25340],{"className":25339,"style":6813},[2084],[1889,25341],{},[1889,25343],{"className":25344},[2367,6726],[1889,25346,25348],{"className":25347},[1938],[1889,25349,25351,25406],{"className":25350},[1892],[1889,25352,25354],{"className":25353},[1896],[1898,25355,25356],{"xmlns":1900,"display":1947},[1902,25357,25358,25403],{},[1905,25359,25360,25362,25364,25366,25372,25374,25380,25382,25388,25390,25398,25400],{},[1908,25361,5314],{},[1908,25363,9682],{},[1955,25365,7183],{},[6567,25367,25368,25370],{},[1969,25369,1971],{},[1969,25371,1990],{},[1955,25373,16294],{},[6567,25375,25376,25378],{},[1969,25377,1971],{},[1969,25379,24715],{},[1955,25381,16294],{},[2783,25383,25384,25386],{},[1969,25385,16129],{},[1969,25387,1990],{},[1955,25389,1957],{},[6567,25391,25392,25395],{},[1969,25393,25394],{},"1296",[1969,25396,25397],{},"400",[1955,25399,1957],{},[1969,25401,25402],{},"3.24",[1912,25404,25405],{"encoding":1914},"RP \\approx \\frac{1}{2} \\times \\frac{1}{200} \\times 36^2 = \\frac{1296}{400} = 3.24",[1889,25407,25409,25430,25507,25584,25632,25709],{"className":25408,"ariaHidden":1919},[1918],[1889,25410,25412,25415,25418,25421,25424,25427],{"className":25411},[1923],[1889,25413],{"className":25414,"style":1928},[1927],[1889,25416,5314],{"className":25417,"style":9718},[1932,1933],[1889,25419,9682],{"className":25420,"style":9722},[1932,1933],[1889,25422],{"className":25423,"style":2043},[2042],[1889,25425,7183],{"className":25426},[2047],[1889,25428],{"className":25429,"style":2043},[2042],[1889,25431,25433,25436,25498,25501,25504],{"className":25432},[1923],[1889,25434],{"className":25435,"style":10595},[1927],[1889,25437,25439,25442,25495],{"className":25438},[1932],[1889,25440],{"className":25441},[2061,6726],[1889,25443,25445],{"className":25444},[6567],[1889,25446,25448,25487],{"className":25447},[2075,2076],[1889,25449,25451,25484],{"className":25450},[2080],[1889,25452,25454,25465,25473],{"className":25453,"style":6739},[2084],[1889,25455,25456,25459],{"style":6742},[1889,25457],{"className":25458,"style":6746},[2092],[1889,25460,25462],{"className":25461},[1932],[1889,25463,1990],{"className":25464},[1932],[1889,25466,25467,25470],{"style":6783},[1889,25468],{"className":25469,"style":6746},[2092],[1889,25471],{"className":25472,"style":6791},[6790],[1889,25474,25475,25478],{"style":6794},[1889,25476],{"className":25477,"style":6746},[2092],[1889,25479,25481],{"className":25480},[1932],[1889,25482,1971],{"className":25483},[1932],[1889,25485,2108],{"className":25486},[2107],[1889,25488,25490],{"className":25489},[2080],[1889,25491,25493],{"className":25492,"style":6813},[2084],[1889,25494],{},[1889,25496],{"className":25497},[2367,6726],[1889,25499],{"className":25500,"style":4041},[2042],[1889,25502,16294],{"className":25503},[4045],[1889,25505],{"className":25506,"style":4041},[2042],[1889,25508,25510,25513,25575,25578,25581],{"className":25509},[1923],[1889,25511],{"className":25512,"style":10595},[1927],[1889,25514,25516,25519,25572],{"className":25515},[1932],[1889,25517],{"className":25518},[2061,6726],[1889,25520,25522],{"className":25521},[6567],[1889,25523,25525,25564],{"className":25524},[2075,2076],[1889,25526,25528,25561],{"className":25527},[2080],[1889,25529,25531,25542,25550],{"className":25530,"style":6739},[2084],[1889,25532,25533,25536],{"style":6742},[1889,25534],{"className":25535,"style":6746},[2092],[1889,25537,25539],{"className":25538},[1932],[1889,25540,24715],{"className":25541},[1932],[1889,25543,25544,25547],{"style":6783},[1889,25545],{"className":25546,"style":6746},[2092],[1889,25548],{"className":25549,"style":6791},[6790],[1889,25551,25552,25555],{"style":6794},[1889,25553],{"className":25554,"style":6746},[2092],[1889,25556,25558],{"className":25557},[1932],[1889,25559,1971],{"className":25560},[1932],[1889,25562,2108],{"className":25563},[2107],[1889,25565,25567],{"className":25566},[2080],[1889,25568,25570],{"className":25569,"style":6813},[2084],[1889,25571],{},[1889,25573],{"className":25574},[2367,6726],[1889,25576],{"className":25577,"style":4041},[2042],[1889,25579,16294],{"className":25580},[4045],[1889,25582],{"className":25583,"style":4041},[2042],[1889,25585,25587,25590,25593,25623,25626,25629],{"className":25586},[1923],[1889,25588],{"className":25589,"style":9057},[1927],[1889,25591,3352],{"className":25592},[1932],[1889,25594,25596,25600],{"className":25595},[1932],[1889,25597,25599],{"className":25598},[1932],"6",[1889,25601,25603],{"className":25602},[2071],[1889,25604,25606],{"className":25605},[2075],[1889,25607,25609],{"className":25608},[2080],[1889,25610,25612],{"className":25611,"style":9057},[2084],[1889,25613,25614,25617],{"style":3045},[1889,25615],{"className":25616,"style":2093},[2092],[1889,25618,25620],{"className":25619},[2097,2098,2099,2100],[1889,25621,1990],{"className":25622},[1932,2100],[1889,25624],{"className":25625,"style":2043},[2042],[1889,25627,1957],{"className":25628},[2047],[1889,25630],{"className":25631,"style":2043},[2042],[1889,25633,25635,25638,25700,25703,25706],{"className":25634},[1923],[1889,25636],{"className":25637,"style":10595},[1927],[1889,25639,25641,25644,25697],{"className":25640},[1932],[1889,25642],{"className":25643},[2061,6726],[1889,25645,25647],{"className":25646},[6567],[1889,25648,25650,25689],{"className":25649},[2075,2076],[1889,25651,25653,25686],{"className":25652},[2080],[1889,25654,25656,25667,25675],{"className":25655,"style":6739},[2084],[1889,25657,25658,25661],{"style":6742},[1889,25659],{"className":25660,"style":6746},[2092],[1889,25662,25664],{"className":25663},[1932],[1889,25665,25397],{"className":25666},[1932],[1889,25668,25669,25672],{"style":6783},[1889,25670],{"className":25671,"style":6746},[2092],[1889,25673],{"className":25674,"style":6791},[6790],[1889,25676,25677,25680],{"style":6794},[1889,25678],{"className":25679,"style":6746},[2092],[1889,25681,25683],{"className":25682},[1932],[1889,25684,25394],{"className":25685},[1932],[1889,25687,2108],{"className":25688},[2107],[1889,25690,25692],{"className":25691},[2080],[1889,25693,25695],{"className":25694,"style":6813},[2084],[1889,25696],{},[1889,25698],{"className":25699},[2367,6726],[1889,25701],{"className":25702,"style":2043},[2042],[1889,25704,1957],{"className":25705},[2047],[1889,25707],{"className":25708,"style":2043},[2042],[1889,25710,25712,25715],{"className":25711},[1923],[1889,25713],{"className":25714,"style":2694},[1927],[1889,25716,25402],{"className":25717},[1932],[1798,25719,25720],{},"与精确值3.37很接近！",[1877,25722,25724],{"id":25723},"例题2-最优保险购买","例题2: 最优保险购买",[1798,25726,25727,25729,25730,16017,25848,16017,25941,16017,25992,16017,26044,26095,26096,2698],{},[1884,25728,23468],{},": ",[1889,25731,25733,25770],{"className":25732},[1892],[1889,25734,25736],{"className":25735},[1896],[1898,25737,25738],{"xmlns":1900},[1902,25739,25740,25767],{},[1905,25741,25742,25744,25746,25748,25750,25752,25754],{},[1908,25743,5308],{},[1955,25745,1961],{"stretchy":1960},[1908,25747,8472],{},[1955,25749,2023],{"stretchy":1960},[1955,25751,1957],{},[1955,25753,3917],{},[2783,25755,25756,25758],{},[1908,25757,11160],{},[1905,25759,25760,25762,25765],{},[1955,25761,3917],{},[1969,25763,25764],{},"0.01",[1908,25766,8472],{},[1912,25768,25769],{"encoding":1914},"u(w) = -e^{-0.01w}",[1889,25771,25773,25800],{"className":25772,"ariaHidden":1919},[1918],[1889,25774,25776,25779,25782,25785,25788,25791,25794,25797],{"className":25775},[1923],[1889,25777],{"className":25778,"style":2057},[1927],[1889,25780,5308],{"className":25781},[1932,1933],[1889,25783,1961],{"className":25784},[2061],[1889,25786,8472],{"className":25787,"style":8687},[1932,1933],[1889,25789,2023],{"className":25790},[2367],[1889,25792],{"className":25793,"style":2043},[2042],[1889,25795,1957],{"className":25796},[2047],[1889,25798],{"className":25799,"style":2043},[2042],[1889,25801,25803,25807,25810],{"className":25802},[1923],[1889,25804],{"className":25805,"style":25806},[1927],"height:0.8974em;vertical-align:-0.0833em;",[1889,25808,3917],{"className":25809},[1932],[1889,25811,25813,25816],{"className":25812},[1932],[1889,25814,11160],{"className":25815},[1932,1933],[1889,25817,25819],{"className":25818},[2071],[1889,25820,25822],{"className":25821},[2075],[1889,25823,25825],{"className":25824},[2080],[1889,25826,25828],{"className":25827,"style":10490},[2084],[1889,25829,25830,25833],{"style":2825},[1889,25831],{"className":25832,"style":2093},[2092],[1889,25834,25836],{"className":25835},[2097,2098,2099,2100],[1889,25837,25839,25842,25845],{"className":25838},[1932,2100],[1889,25840,3917],{"className":25841},[1932,2100],[1889,25843,25764],{"className":25844},[1932,2100],[1889,25846,8472],{"className":25847,"style":8687},[1932,1933,2100],[1889,25849,25851,25874],{"className":25850},[1892],[1889,25852,25854],{"className":25853},[1896],[1898,25855,25856],{"xmlns":1900},[1902,25857,25858,25871],{},[1905,25859,25860,25866,25868],{},[1963,25861,25862,25864],{},[1908,25863,8472],{},[1969,25865,3819],{},[1955,25867,1957],{},[1969,25869,25870],{},"1000",[1912,25872,25873],{"encoding":1914},"w_0 = 1000",[1889,25875,25877,25932],{"className":25876,"ariaHidden":1919},[1918],[1889,25878,25880,25883,25923,25926,25929],{"className":25879},[1923],[1889,25881],{"className":25882,"style":2475},[1927],[1889,25884,25886,25889],{"className":25885},[1932],[1889,25887,8472],{"className":25888,"style":8687},[1932,1933],[1889,25890,25892],{"className":25891},[2071],[1889,25893,25895,25915],{"className":25894},[2075,2076],[1889,25896,25898,25912],{"className":25897},[2080],[1889,25899,25901],{"className":25900,"style":2085},[2084],[1889,25902,25903,25906],{"style":12188},[1889,25904],{"className":25905,"style":2093},[2092],[1889,25907,25909],{"className":25908},[2097,2098,2099,2100],[1889,25910,3819],{"className":25911},[1932,2100],[1889,25913,2108],{"className":25914},[2107],[1889,25916,25918],{"className":25917},[2080],[1889,25919,25921],{"className":25920,"style":2115},[2084],[1889,25922],{},[1889,25924],{"className":25925,"style":2043},[2042],[1889,25927,1957],{"className":25928},[2047],[1889,25930],{"className":25931,"style":2043},[2042],[1889,25933,25935,25938],{"className":25934},[1923],[1889,25936],{"className":25937,"style":2694},[1927],[1889,25939,25870],{"className":25940},[1932],[1889,25942,25944,25962],{"className":25943},[1892],[1889,25945,25947],{"className":25946},[1896],[1898,25948,25949],{"xmlns":1900},[1902,25950,25951,25959],{},[1905,25952,25953,25955,25957],{},[1908,25954,1910],{},[1955,25956,1957],{},[1969,25958,25397],{},[1912,25960,25961],{"encoding":1914},"L = 400",[1889,25963,25965,25983],{"className":25964,"ariaHidden":1919},[1918],[1889,25966,25968,25971,25974,25977,25980],{"className":25967},[1923],[1889,25969],{"className":25970,"style":1928},[1927],[1889,25972,1910],{"className":25973},[1932,1933],[1889,25975],{"className":25976,"style":2043},[2042],[1889,25978,1957],{"className":25979},[2047],[1889,25981],{"className":25982,"style":2043},[2042],[1889,25984,25986,25989],{"className":25985},[1923],[1889,25987],{"className":25988,"style":2694},[1927],[1889,25990,25397],{"className":25991},[1932],[1889,25993,25995,26014],{"className":25994},[1892],[1889,25996,25998],{"className":25997},[1896],[1898,25999,26000],{"xmlns":1900},[1902,26001,26002,26011],{},[1905,26003,26004,26006,26008],{},[1908,26005,1798],{},[1955,26007,1957],{},[1969,26009,26010],{},"0.2",[1912,26012,26013],{"encoding":1914},"p = 0.2",[1889,26015,26017,26035],{"className":26016,"ariaHidden":1919},[1918],[1889,26018,26020,26023,26026,26029,26032],{"className":26019},[1923],[1889,26021],{"className":26022,"style":2402},[1927],[1889,26024,1798],{"className":26025},[1932,1933],[1889,26027],{"className":26028,"style":2043},[2042],[1889,26030,1957],{"className":26031},[2047],[1889,26033],{"className":26034,"style":2043},[2042],[1889,26036,26038,26041],{"className":26037},[1923],[1889,26039],{"className":26040,"style":2694},[1927],[1889,26042,26010],{"className":26043},[1932],[1889,26045,26047,26065],{"className":26046},[1892],[1889,26048,26050],{"className":26049},[1896],[1898,26051,26052],{"xmlns":1900},[1902,26053,26054,26062],{},[1905,26055,26056,26058,26060],{},[1908,26057,12757],{},[1955,26059,1957],{},[1969,26061,16181],{},[1912,26063,26064],{"encoding":1914},"\\pi = 0.25",[1889,26066,26068,26086],{"className":26067,"ariaHidden":1919},[1918],[1889,26069,26071,26074,26077,26080,26083],{"className":26070},[1923],[1889,26072],{"className":26073,"style":5332},[1927],[1889,26075,12757],{"className":26076,"style":6310},[1932,1933],[1889,26078],{"className":26079,"style":2043},[2042],[1889,26081,1957],{"className":26082},[2047],[1889,26084],{"className":26085,"style":2043},[2042],[1889,26087,26089,26092],{"className":26088},[1923],[1889,26090],{"className":26091,"style":2694},[1927],[1889,26093,16181],{"className":26094},[1932],"。求最优保险额",[1889,26097,26099,26117],{"className":26098},[1892],[1889,26100,26102],{"className":26101},[1896],[1898,26103,26104],{"xmlns":1900},[1902,26105,26106,26114],{},[1905,26107,26108],{},[2783,26109,26110,26112],{},[1908,26111,1967],{},[1955,26113,15587],{},[1912,26115,26116],{"encoding":1914},"x^*",[1889,26118,26120],{"className":26119,"ariaHidden":1919},[1918],[1889,26121,26123,26126],{"className":26122},[1923],[1889,26124],{"className":26125,"style":15604},[1927],[1889,26127,26129,26132],{"className":26128},[1932],[1889,26130,1967],{"className":26131},[1932,1933],[1889,26133,26135],{"className":26134},[2071],[1889,26136,26138],{"className":26137},[2075],[1889,26139,26141],{"className":26140},[2080],[1889,26142,26144],{"className":26143,"style":15604},[2084],[1889,26145,26146,26149],{"style":2825},[1889,26147],{"className":26148,"style":2093},[2092],[1889,26150,26152],{"className":26151},[2097,2098,2099,2100],[1889,26153,15587],{"className":26154},[4045,2100],[1798,26156,26157,2704],{},[1884,26158,23657],{},[1798,26160,16269],{},[1889,26162,26164],{"className":26163},[1938],[1889,26165,26167,26261],{"className":26166},[1892],[1889,26168,26170],{"className":26169},[1896],[1898,26171,26172],{"xmlns":1900,"display":1947},[1902,26173,26174,26258],{},[1905,26175,26176,26178,26180,26182,26184,26186,26188,26194,26196,26202,26204,26206,26208,26210,26212,26214,26216,26218,26220,26222,26224,26230,26232,26238,26240,26242,26244,26246,26248,26250,26252,26254,26256],{},[1955,26177,1961],{"stretchy":1960},[1969,26179,1971],{},[1955,26181,3917],{},[1908,26183,1798],{},[1955,26185,2023],{"stretchy":1960},[1908,26187,12757],{},[2783,26189,26190,26192],{},[1908,26191,5308],{},[1955,26193,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,26195,1961],{"stretchy":1960},[1963,26197,26198,26200],{},[1908,26199,8472],{},[1969,26201,3819],{},[1955,26203,3917],{},[1908,26205,12757],{},[1908,26207,1967],{},[1955,26209,2023],{"stretchy":1960},[1955,26211,1957],{},[1908,26213,1798],{},[1955,26215,1961],{"stretchy":1960},[1969,26217,1971],{},[1955,26219,3917],{},[1908,26221,12757],{},[1955,26223,2023],{"stretchy":1960},[2783,26225,26226,26228],{},[1908,26227,5308],{},[1955,26229,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,26231,1961],{"stretchy":1960},[1963,26233,26234,26236],{},[1908,26235,8472],{},[1969,26237,3819],{},[1955,26239,3917],{},[1908,26241,1910],{},[1955,26243,3910],{},[1955,26245,1961],{"stretchy":1960},[1969,26247,1971],{},[1955,26249,3917],{},[1908,26251,12757],{},[1955,26253,2023],{"stretchy":1960},[1908,26255,1967],{},[1955,26257,2023],{"stretchy":1960},[1912,26259,26260],{"encoding":1914},"(1-p)\\pi u'(w_0 - \\pi x) = p(1-\\pi) u'(w_0 - L + (1-\\pi)x)",[1889,26262,26264,26285,26384,26408,26432,26528,26546,26567],{"className":26263,"ariaHidden":1919},[1918],[1889,26265,26267,26270,26273,26276,26279,26282],{"className":26266},[1923],[1889,26268],{"className":26269,"style":2057},[1927],[1889,26271,1961],{"className":26272},[2061],[1889,26274,1971],{"className":26275},[1932],[1889,26277],{"className":26278,"style":4041},[2042],[1889,26280,3917],{"className":26281},[4045],[1889,26283],{"className":26284,"style":4041},[2042],[1889,26286,26288,26291,26294,26297,26300,26332,26335,26375,26378,26381],{"className":26287},[1923],[1889,26289],{"className":26290,"style":18549},[1927],[1889,26292,1798],{"className":26293},[1932,1933],[1889,26295,2023],{"className":26296},[2367],[1889,26298,12757],{"className":26299,"style":6310},[1932,1933],[1889,26301,26303,26306],{"className":26302},[1932],[1889,26304,5308],{"className":26305},[1932,1933],[1889,26307,26309],{"className":26308},[2071],[1889,26310,26312],{"className":26311},[2075],[1889,26313,26315],{"className":26314},[2080],[1889,26316,26318],{"className":26317,"style":3042},[2084],[1889,26319,26320,26323],{"style":3045},[1889,26321],{"className":26322,"style":2093},[2092],[1889,26324,26326],{"className":26325},[2097,2098,2099,2100],[1889,26327,26329],{"className":26328},[1932,2100],[1889,26330,2791],{"className":26331},[1932,2100],[1889,26333,1961],{"className":26334},[2061],[1889,26336,26338,26341],{"className":26337},[1932],[1889,26339,8472],{"className":26340,"style":8687},[1932,1933],[1889,26342,26344],{"className":26343},[2071],[1889,26345,26347,26367],{"className":26346},[2075,2076],[1889,26348,26350,26364],{"className":26349},[2080],[1889,26351,26353],{"className":26352,"style":2085},[2084],[1889,26354,26355,26358],{"style":12188},[1889,26356],{"className":26357,"style":2093},[2092],[1889,26359,26361],{"className":26360},[2097,2098,2099,2100],[1889,26362,3819],{"className":26363},[1932,2100],[1889,26365,2108],{"className":26366},[2107],[1889,26368,26370],{"className":26369},[2080],[1889,26371,26373],{"className":26372,"style":2115},[2084],[1889,26374],{},[1889,26376],{"className":26377,"style":4041},[2042],[1889,26379,3917],{"className":26380},[4045],[1889,26382],{"className":26383,"style":4041},[2042],[1889,26385,26387,26390,26393,26396,26399,26402,26405],{"className":26386},[1923],[1889,26388],{"className":26389,"style":2057},[1927],[1889,26391,12757],{"className":26392,"style":6310},[1932,1933],[1889,26394,1967],{"className":26395},[1932,1933],[1889,26397,2023],{"className":26398},[2367],[1889,26400],{"className":26401,"style":2043},[2042],[1889,26403,1957],{"className":26404},[2047],[1889,26406],{"className":26407,"style":2043},[2042],[1889,26409,26411,26414,26417,26420,26423,26426,26429],{"className":26410},[1923],[1889,26412],{"className":26413,"style":2057},[1927],[1889,26415,1798],{"className":26416},[1932,1933],[1889,26418,1961],{"className":26419},[2061],[1889,26421,1971],{"className":26422},[1932],[1889,26424],{"className":26425,"style":4041},[2042],[1889,26427,3917],{"className":26428},[4045],[1889,26430],{"className":26431,"style":4041},[2042],[1889,26433,26435,26438,26441,26444,26476,26479,26519,26522,26525],{"className":26434},[1923],[1889,26436],{"className":26437,"style":18549},[1927],[1889,26439,12757],{"className":26440,"style":6310},[1932,1933],[1889,26442,2023],{"className":26443},[2367],[1889,26445,26447,26450],{"className":26446},[1932],[1889,26448,5308],{"className":26449},[1932,1933],[1889,26451,26453],{"className":26452},[2071],[1889,26454,26456],{"className":26455},[2075],[1889,26457,26459],{"className":26458},[2080],[1889,26460,26462],{"className":26461,"style":3042},[2084],[1889,26463,26464,26467],{"style":3045},[1889,26465],{"className":26466,"style":2093},[2092],[1889,26468,26470],{"className":26469},[2097,2098,2099,2100],[1889,26471,26473],{"className":26472},[1932,2100],[1889,26474,2791],{"className":26475},[1932,2100],[1889,26477,1961],{"className":26478},[2061],[1889,26480,26482,26485],{"className":26481},[1932],[1889,26483,8472],{"className":26484,"style":8687},[1932,1933],[1889,26486,26488],{"className":26487},[2071],[1889,26489,26491,26511],{"className":26490},[2075,2076],[1889,26492,26494,26508],{"className":26493},[2080],[1889,26495,26497],{"className":26496,"style":2085},[2084],[1889,26498,26499,26502],{"style":12188},[1889,26500],{"className":26501,"style":2093},[2092],[1889,26503,26505],{"className":26504},[2097,2098,2099,2100],[1889,26506,3819],{"className":26507},[1932,2100],[1889,26509,2108],{"className":26510},[2107],[1889,26512,26514],{"className":26513},[2080],[1889,26515,26517],{"className":26516,"style":2115},[2084],[1889,26518],{},[1889,26520],{"className":26521,"style":4041},[2042],[1889,26523,3917],{"className":26524},[4045],[1889,26526],{"className":26527,"style":4041},[2042],[1889,26529,26531,26534,26537,26540,26543],{"className":26530},[1923],[1889,26532],{"className":26533,"style":13190},[1927],[1889,26535,1910],{"className":26536},[1932,1933],[1889,26538],{"className":26539,"style":4041},[2042],[1889,26541,3910],{"className":26542},[4045],[1889,26544],{"className":26545,"style":4041},[2042],[1889,26547,26549,26552,26555,26558,26561,26564],{"className":26548},[1923],[1889,26550],{"className":26551,"style":2057},[1927],[1889,26553,1961],{"className":26554},[2061],[1889,26556,1971],{"className":26557},[1932],[1889,26559],{"className":26560,"style":4041},[2042],[1889,26562,3917],{"className":26563},[4045],[1889,26565],{"className":26566,"style":4041},[2042],[1889,26568,26570,26573,26576,26579,26582],{"className":26569},[1923],[1889,26571],{"className":26572,"style":2057},[1927],[1889,26574,12757],{"className":26575,"style":6310},[1932,1933],[1889,26577,2023],{"className":26578},[2367],[1889,26580,1967],{"className":26581},[1932,1933],[1889,26583,2023],{"className":26584},[2367],[1798,26586,26587,26588,4831],{},"对于负指数效用，",[1889,26589,26591,26631],{"className":26590},[1892],[1889,26592,26594],{"className":26593},[1896],[1898,26595,26596],{"xmlns":1900},[1902,26597,26598,26628],{},[1905,26599,26600,26606,26608,26610,26612,26614,26616],{},[2783,26601,26602,26604],{},[1908,26603,5308],{},[1955,26605,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1955,26607,1961],{"stretchy":1960},[1908,26609,8472],{},[1955,26611,2023],{"stretchy":1960},[1955,26613,1957],{},[1969,26615,25764],{},[2783,26617,26618,26620],{},[1908,26619,11160],{},[1905,26621,26622,26624,26626],{},[1955,26623,3917],{},[1969,26625,25764],{},[1908,26627,8472],{},[1912,26629,26630],{"encoding":1914},"u'(w) = 0.01e^{-0.01w}",[1889,26632,26634,26690],{"className":26633,"ariaHidden":1919},[1918],[1889,26635,26637,26640,26672,26675,26678,26681,26684,26687],{"className":26636},[1923],[1889,26638],{"className":26639,"style":6134},[1927],[1889,26641,26643,26646],{"className":26642},[1932],[1889,26644,5308],{"className":26645},[1932,1933],[1889,26647,26649],{"className":26648},[2071],[1889,26650,26652],{"className":26651},[2075],[1889,26653,26655],{"className":26654},[2080],[1889,26656,26658],{"className":26657,"style":2804},[2084],[1889,26659,26660,26663],{"style":2825},[1889,26661],{"className":26662,"style":2093},[2092],[1889,26664,26666],{"className":26665},[2097,2098,2099,2100],[1889,26667,26669],{"className":26668},[1932,2100],[1889,26670,2791],{"className":26671},[1932,2100],[1889,26673,1961],{"className":26674},[2061],[1889,26676,8472],{"className":26677,"style":8687},[1932,1933],[1889,26679,2023],{"className":26680},[2367],[1889,26682],{"className":26683,"style":2043},[2042],[1889,26685,1957],{"className":26686},[2047],[1889,26688],{"className":26689,"style":2043},[2042],[1889,26691,26693,26696,26699],{"className":26692},[1923],[1889,26694],{"className":26695,"style":10490},[1927],[1889,26697,25764],{"className":26698},[1932],[1889,26700,26702,26705],{"className":26701},[1932],[1889,26703,11160],{"className":26704},[1932,1933],[1889,26706,26708],{"className":26707},[2071],[1889,26709,26711],{"className":26710},[2075],[1889,26712,26714],{"className":26713},[2080],[1889,26715,26717],{"className":26716,"style":10490},[2084],[1889,26718,26719,26722],{"style":2825},[1889,26720],{"className":26721,"style":2093},[2092],[1889,26723,26725],{"className":26724},[2097,2098,2099,2100],[1889,26726,26728,26731,26734],{"className":26727},[1932,2100],[1889,26729,3917],{"className":26730},[1932,2100],[1889,26732,25764],{"className":26733},[1932,2100],[1889,26735,8472],{"className":26736,"style":8687},[1932,1933,2100],[1889,26738,26740],{"className":26739},[1938],[1889,26741,26743,26819],{"className":26742},[1892],[1889,26744,26746],{"className":26745},[1896],[1898,26747,26748],{"xmlns":1900,"display":1947},[1902,26749,26750,26816],{},[1905,26751,26752,26755,26757,26759,26761,26783,26785,26787,26789,26791,26793],{},[1969,26753,26754],{},"0.8",[1955,26756,16294],{},[1969,26758,16181],{},[1955,26760,16294],{},[2783,26762,26763,26765],{},[1908,26764,11160],{},[1905,26766,26767,26769,26771,26773,26775,26777,26779,26781],{},[1955,26768,3917],{},[1969,26770,25764],{},[1955,26772,1961],{"stretchy":1960},[1969,26774,25870],{},[1955,26776,3917],{},[1969,26778,16181],{},[1908,26780,1967],{},[1955,26782,2023],{"stretchy":1960},[1955,26784,1957],{},[1969,26786,26010],{},[1955,26788,16294],{},[1969,26790,16291],{},[1955,26792,16294],{},[2783,26794,26795,26797],{},[1908,26796,11160],{},[1905,26798,26799,26801,26803,26805,26808,26810,26812,26814],{},[1955,26800,3917],{},[1969,26802,25764],{},[1955,26804,1961],{"stretchy":1960},[1969,26806,26807],{},"600",[1955,26809,3910],{},[1969,26811,16291],{},[1908,26813,1967],{},[1955,26815,2023],{"stretchy":1960},[1912,26817,26818],{"encoding":1914},"0.8 \\times 0.25 \\times e^{-0.01(1000-0.25x)} = 0.2 \\times 0.75 \\times e^{-0.01(600+0.75x)}",[1889,26820,26822,26840,26858,26927,26945,26963],{"className":26821,"ariaHidden":1919},[1918],[1889,26823,26825,26828,26831,26834,26837],{"className":26824},[1923],[1889,26826],{"className":26827,"style":12913},[1927],[1889,26829,26754],{"className":26830},[1932],[1889,26832],{"className":26833,"style":4041},[2042],[1889,26835,16294],{"className":26836},[4045],[1889,26838],{"className":26839,"style":4041},[2042],[1889,26841,26843,26846,26849,26852,26855],{"className":26842},[1923],[1889,26844],{"className":26845,"style":12913},[1927],[1889,26847,16181],{"className":26848},[1932],[1889,26850],{"className":26851,"style":4041},[2042],[1889,26853,16294],{"className":26854},[4045],[1889,26856],{"className":26857,"style":4041},[2042],[1889,26859,26861,26865,26918,26921,26924],{"className":26860},[1923],[1889,26862],{"className":26863,"style":26864},[1927],"height:0.938em;",[1889,26866,26868,26871],{"className":26867},[1932],[1889,26869,11160],{"className":26870},[1932,1933],[1889,26872,26874],{"className":26873},[2071],[1889,26875,26877],{"className":26876},[2075],[1889,26878,26880],{"className":26879},[2080],[1889,26881,26883],{"className":26882,"style":26864},[2084],[1889,26884,26885,26888],{"style":3045},[1889,26886],{"className":26887,"style":2093},[2092],[1889,26889,26891],{"className":26890},[2097,2098,2099,2100],[1889,26892,26894,26897,26900,26903,26906,26909,26912,26915],{"className":26893},[1932,2100],[1889,26895,3917],{"className":26896},[1932,2100],[1889,26898,25764],{"className":26899},[1932,2100],[1889,26901,1961],{"className":26902},[2061,2100],[1889,26904,25870],{"className":26905},[1932,2100],[1889,26907,3917],{"className":26908},[4045,2100],[1889,26910,16181],{"className":26911},[1932,2100],[1889,26913,1967],{"className":26914},[1932,1933,2100],[1889,26916,2023],{"className":26917},[2367,2100],[1889,26919],{"className":26920,"style":2043},[2042],[1889,26922,1957],{"className":26923},[2047],[1889,26925],{"className":26926,"style":2043},[2042],[1889,26928,26930,26933,26936,26939,26942],{"className":26929},[1923],[1889,26931],{"className":26932,"style":12913},[1927],[1889,26934,26010],{"className":26935},[1932],[1889,26937],{"className":26938,"style":4041},[2042],[1889,26940,16294],{"className":26941},[4045],[1889,26943],{"className":26944,"style":4041},[2042],[1889,26946,26948,26951,26954,26957,26960],{"className":26947},[1923],[1889,26949],{"className":26950,"style":12913},[1927],[1889,26952,16291],{"className":26953},[1932],[1889,26955],{"className":26956,"style":4041},[2042],[1889,26958,16294],{"className":26959},[4045],[1889,26961],{"className":26962,"style":4041},[2042],[1889,26964,26966,26969],{"className":26965},[1923],[1889,26967],{"className":26968,"style":26864},[1927],[1889,26970,26972,26975],{"className":26971},[1932],[1889,26973,11160],{"className":26974},[1932,1933],[1889,26976,26978],{"className":26977},[2071],[1889,26979,26981],{"className":26980},[2075],[1889,26982,26984],{"className":26983},[2080],[1889,26985,26987],{"className":26986,"style":26864},[2084],[1889,26988,26989,26992],{"style":3045},[1889,26990],{"className":26991,"style":2093},[2092],[1889,26993,26995],{"className":26994},[2097,2098,2099,2100],[1889,26996,26998,27001,27004,27007,27010,27013,27016,27019],{"className":26997},[1932,2100],[1889,26999,3917],{"className":27000},[1932,2100],[1889,27002,25764],{"className":27003},[1932,2100],[1889,27005,1961],{"className":27006},[2061,2100],[1889,27008,26807],{"className":27009},[1932,2100],[1889,27011,3910],{"className":27012},[4045,2100],[1889,27014,16291],{"className":27015},[1932,2100],[1889,27017,1967],{"className":27018},[1932,1933,2100],[1889,27020,2023],{"className":27021},[2367,2100],[1889,27023,27025],{"className":27024},[1938],[1889,27026,27028,27082],{"className":27027},[1892],[1889,27029,27031],{"className":27030},[1896],[1898,27032,27033],{"xmlns":1900,"display":1947},[1902,27034,27035,27079],{},[1905,27036,27037,27039,27057,27059,27062],{},[1969,27038,26010],{},[2783,27040,27041,27043],{},[1908,27042,11160],{},[1905,27044,27045,27047,27050,27052,27055],{},[1955,27046,3917],{},[1969,27048,27049],{},"10",[1955,27051,3910],{},[1969,27053,27054],{},"0.0025",[1908,27056,1967],{},[1955,27058,1957],{},[1969,27060,27061],{},"0.15",[2783,27063,27064,27066],{},[1908,27065,11160],{},[1905,27067,27068,27070,27072,27074,27077],{},[1955,27069,3917],{},[1969,27071,25599],{},[1955,27073,3910],{},[1969,27075,27076],{},"0.0075",[1908,27078,1967],{},[1912,27080,27081],{"encoding":1914},"0.2 e^{-10+0.0025x} = 0.15 e^{-6+0.0075x}",[1889,27083,27085,27147],{"className":27084,"ariaHidden":1919},[1918],[1889,27086,27088,27091,27094,27138,27141,27144],{"className":27087},[1923],[1889,27089],{"className":27090,"style":9057},[1927],[1889,27092,26010],{"className":27093},[1932],[1889,27095,27097,27100],{"className":27096},[1932],[1889,27098,11160],{"className":27099},[1932,1933],[1889,27101,27103],{"className":27102},[2071],[1889,27104,27106],{"className":27105},[2075],[1889,27107,27109],{"className":27108},[2080],[1889,27110,27112],{"className":27111,"style":9057},[2084],[1889,27113,27114,27117],{"style":3045},[1889,27115],{"className":27116,"style":2093},[2092],[1889,27118,27120],{"className":27119},[2097,2098,2099,2100],[1889,27121,27123,27126,27129,27132,27135],{"className":27122},[1932,2100],[1889,27124,3917],{"className":27125},[1932,2100],[1889,27127,27049],{"className":27128},[1932,2100],[1889,27130,3910],{"className":27131},[4045,2100],[1889,27133,27054],{"className":27134},[1932,2100],[1889,27136,1967],{"className":27137},[1932,1933,2100],[1889,27139],{"className":27140,"style":2043},[2042],[1889,27142,1957],{"className":27143},[2047],[1889,27145],{"className":27146,"style":2043},[2042],[1889,27148,27150,27153,27156],{"className":27149},[1923],[1889,27151],{"className":27152,"style":9057},[1927],[1889,27154,27061],{"className":27155},[1932],[1889,27157,27159,27162],{"className":27158},[1932],[1889,27160,11160],{"className":27161},[1932,1933],[1889,27163,27165],{"className":27164},[2071],[1889,27166,27168],{"className":27167},[2075],[1889,27169,27171],{"className":27170},[2080],[1889,27172,27174],{"className":27173,"style":9057},[2084],[1889,27175,27176,27179],{"style":3045},[1889,27177],{"className":27178,"style":2093},[2092],[1889,27180,27182],{"className":27181},[2097,2098,2099,2100],[1889,27183,27185,27188,27191,27194,27197],{"className":27184},[1932,2100],[1889,27186,3917],{"className":27187},[1932,2100],[1889,27189,25599],{"className":27190},[1932,2100],[1889,27192,3910],{"className":27193},[4045,2100],[1889,27195,27076],{"className":27196},[1932,2100],[1889,27198,1967],{"className":27199},[1932,1933,2100],[1889,27201,27203],{"className":27202},[1938],[1889,27204,27206,27241],{"className":27205},[1892],[1889,27207,27209],{"className":27208},[1896],[1898,27210,27211],{"xmlns":1900,"display":1947},[1902,27212,27213,27238],{},[1905,27214,27215,27221,27223],{},[6567,27216,27217,27219],{},[1969,27218,26010],{},[1969,27220,27061],{},[1955,27222,1957],{},[2783,27224,27225,27227],{},[1908,27226,11160],{},[1905,27228,27229,27231,27233,27236],{},[1969,27230,24658],{},[1955,27232,3917],{},[1969,27234,27235],{},"0.005",[1908,27237,1967],{},[1912,27239,27240],{"encoding":1914},"\\frac{0.2}{0.15} = e^{4-0.005x}",[1889,27242,27244,27321],{"className":27243,"ariaHidden":1919},[1918],[1889,27245,27247,27250,27312,27315,27318],{"className":27246},[1923],[1889,27248],{"className":27249,"style":10595},[1927],[1889,27251,27253,27256,27309],{"className":27252},[1932],[1889,27254],{"className":27255},[2061,6726],[1889,27257,27259],{"className":27258},[6567],[1889,27260,27262,27301],{"className":27261},[2075,2076],[1889,27263,27265,27298],{"className":27264},[2080],[1889,27266,27268,27279,27287],{"className":27267,"style":6739},[2084],[1889,27269,27270,27273],{"style":6742},[1889,27271],{"className":27272,"style":6746},[2092],[1889,27274,27276],{"className":27275},[1932],[1889,27277,27061],{"className":27278},[1932],[1889,27280,27281,27284],{"style":6783},[1889,27282],{"className":27283,"style":6746},[2092],[1889,27285],{"className":27286,"style":6791},[6790],[1889,27288,27289,27292],{"style":6794},[1889,27290],{"className":27291,"style":6746},[2092],[1889,27293,27295],{"className":27294},[1932],[1889,27296,26010],{"className":27297},[1932],[1889,27299,2108],{"className":27300},[2107],[1889,27302,27304],{"className":27303},[2080],[1889,27305,27307],{"className":27306,"style":6813},[2084],[1889,27308],{},[1889,27310],{"className":27311},[2367,6726],[1889,27313],{"className":27314,"style":2043},[2042],[1889,27316,1957],{"className":27317},[2047],[1889,27319],{"className":27320,"style":2043},[2042],[1889,27322,27324,27327],{"className":27323},[1923],[1889,27325],{"className":27326,"style":9057},[1927],[1889,27328,27330,27333],{"className":27329},[1932],[1889,27331,11160],{"className":27332},[1932,1933],[1889,27334,27336],{"className":27335},[2071],[1889,27337,27339],{"className":27338},[2075],[1889,27340,27342],{"className":27341},[2080],[1889,27343,27345],{"className":27344,"style":9057},[2084],[1889,27346,27347,27350],{"style":3045},[1889,27348],{"className":27349,"style":2093},[2092],[1889,27351,27353],{"className":27352},[2097,2098,2099,2100],[1889,27354,27356,27359,27362,27365],{"className":27355},[1932,2100],[1889,27357,24658],{"className":27358},[1932,2100],[1889,27360,3917],{"className":27361},[4045,2100],[1889,27363,27235],{"className":27364},[1932,2100],[1889,27366,1967],{"className":27367},[1932,1933,2100],[1889,27369,27371],{"className":27370},[1938],[1889,27372,27374,27410],{"className":27373},[1892],[1889,27375,27377],{"className":27376},[1896],[1898,27378,27379],{"xmlns":1900,"display":1947},[1902,27380,27381,27407],{},[1905,27382,27383,27385,27387,27389,27391,27393,27395,27397,27399,27401,27403,27405],{},[1908,27384,7007],{},[1955,27386,7010],{},[1955,27388,1961],{"stretchy":1960},[1969,27390,24658],{},[1908,27392,11106],{"mathvariant":2789},[1969,27394,3352],{},[1955,27396,2023],{"stretchy":1960},[1955,27398,1957],{},[1969,27400,24658],{},[1955,27402,3917],{},[1969,27404,27235],{},[1908,27406,1967],{},[1912,27408,27409],{"encoding":1914},"\\ln(4\u002F3) = 4 - 0.005x",[1889,27411,27413,27441,27459],{"className":27412,"ariaHidden":1919},[1918],[1889,27414,27416,27419,27422,27425,27429,27432,27435,27438],{"className":27415},[1923],[1889,27417],{"className":27418,"style":2057},[1927],[1889,27420,7007],{"className":27421},[2571],[1889,27423,1961],{"className":27424},[2061],[1889,27426,27428],{"className":27427},[1932],"4\u002F3",[1889,27430,2023],{"className":27431},[2367],[1889,27433],{"className":27434,"style":2043},[2042],[1889,27436,1957],{"className":27437},[2047],[1889,27439],{"className":27440,"style":2043},[2042],[1889,27442,27444,27447,27450,27453,27456],{"className":27443},[1923],[1889,27445],{"className":27446,"style":12913},[1927],[1889,27448,24658],{"className":27449},[1932],[1889,27451],{"className":27452,"style":4041},[2042],[1889,27454,3917],{"className":27455},[4045],[1889,27457],{"className":27458,"style":4041},[2042],[1889,27460,27462,27465,27468],{"className":27461},[1923],[1889,27463],{"className":27464,"style":2694},[1927],[1889,27466,27235],{"className":27467},[1932],[1889,27469,1967],{"className":27470},[1932,1933],[1889,27472,27474],{"className":27473},[1938],[1889,27475,27477,27541],{"className":27476},[1892],[1889,27478,27480],{"className":27479},[1896],[1898,27481,27482],{"xmlns":1900,"display":1947},[1902,27483,27484,27538],{},[1905,27485,27486,27492,27494,27518,27520,27533,27535],{},[2783,27487,27488,27490],{},[1908,27489,1967],{},[1955,27491,15587],{},[1955,27493,1957],{},[6567,27495,27496,27516],{},[1905,27497,27498,27500,27502,27504,27506,27508,27510,27512,27514],{},[1969,27499,24658],{},[1955,27501,3917],{},[1908,27503,7007],{},[1955,27505,7010],{},[1955,27507,1961],{"stretchy":1960},[1969,27509,24658],{},[1908,27511,11106],{"mathvariant":2789},[1969,27513,3352],{},[1955,27515,2023],{"stretchy":1960},[1969,27517,27235],{},[1955,27519,1957],{},[6567,27521,27522,27531],{},[1905,27523,27524,27526,27528],{},[1969,27525,24658],{},[1955,27527,3917],{},[1969,27529,27530],{},"0.288",[1969,27532,27235],{},[1955,27534,1957],{},[1969,27536,27537],{},"742.4",[1912,27539,27540],{"encoding":1914},"x^* = \\frac{4 - \\ln(4\u002F3)}{0.005} = \\frac{4 - 0.288}{0.005} = 742.4",[1889,27542,27544,27588,27688,27777],{"className":27543,"ariaHidden":1919},[1918],[1889,27545,27547,27550,27579,27582,27585],{"className":27546},[1923],[1889,27548],{"className":27549,"style":20643},[1927],[1889,27551,27553,27556],{"className":27552},[1932],[1889,27554,1967],{"className":27555},[1932,1933],[1889,27557,27559],{"className":27558},[2071],[1889,27560,27562],{"className":27561},[2075],[1889,27563,27565],{"className":27564},[2080],[1889,27566,27568],{"className":27567,"style":20643},[2084],[1889,27569,27570,27573],{"style":3045},[1889,27571],{"className":27572,"style":2093},[2092],[1889,27574,27576],{"className":27575},[2097,2098,2099,2100],[1889,27577,15587],{"className":27578},[4045,2100],[1889,27580],{"className":27581,"style":2043},[2042],[1889,27583,1957],{"className":27584},[2047],[1889,27586],{"className":27587,"style":2043},[2042],[1889,27589,27591,27595,27679,27682,27685],{"className":27590},[1923],[1889,27592],{"className":27593,"style":27594},[1927],"height:2.113em;vertical-align:-0.686em;",[1889,27596,27598,27601,27676],{"className":27597},[1932],[1889,27599],{"className":27600},[2061,6726],[1889,27602,27604],{"className":27603},[6567],[1889,27605,27607,27668],{"className":27606},[2075,2076],[1889,27608,27610,27665],{"className":27609},[2080],[1889,27611,27614,27625,27633],{"className":27612,"style":27613},[2084],"height:1.427em;",[1889,27615,27616,27619],{"style":6742},[1889,27617],{"className":27618,"style":6746},[2092],[1889,27620,27622],{"className":27621},[1932],[1889,27623,27235],{"className":27624},[1932],[1889,27626,27627,27630],{"style":6783},[1889,27628],{"className":27629,"style":6746},[2092],[1889,27631],{"className":27632,"style":6791},[6790],[1889,27634,27635,27638],{"style":6794},[1889,27636],{"className":27637,"style":6746},[2092],[1889,27639,27641,27644,27647,27650,27653,27656,27659,27662],{"className":27640},[1932],[1889,27642,24658],{"className":27643},[1932],[1889,27645],{"className":27646,"style":4041},[2042],[1889,27648,3917],{"className":27649},[4045],[1889,27651],{"className":27652,"style":4041},[2042],[1889,27654,7007],{"className":27655},[2571],[1889,27657,1961],{"className":27658},[2061],[1889,27660,27428],{"className":27661},[1932],[1889,27663,2023],{"className":27664},[2367],[1889,27666,2108],{"className":27667},[2107],[1889,27669,27671],{"className":27670},[2080],[1889,27672,27674],{"className":27673,"style":6813},[2084],[1889,27675],{},[1889,27677],{"className":27678},[2367,6726],[1889,27680],{"className":27681,"style":2043},[2042],[1889,27683,1957],{"className":27684},[2047],[1889,27686],{"className":27687,"style":2043},[2042],[1889,27689,27691,27694,27768,27771,27774],{"className":27690},[1923],[1889,27692],{"className":27693,"style":10595},[1927],[1889,27695,27697,27700,27765],{"className":27696},[1932],[1889,27698],{"className":27699},[2061,6726],[1889,27701,27703],{"className":27702},[6567],[1889,27704,27706,27757],{"className":27705},[2075,2076],[1889,27707,27709,27754],{"className":27708},[2080],[1889,27710,27712,27723,27731],{"className":27711,"style":6739},[2084],[1889,27713,27714,27717],{"style":6742},[1889,27715],{"className":27716,"style":6746},[2092],[1889,27718,27720],{"className":27719},[1932],[1889,27721,27235],{"className":27722},[1932],[1889,27724,27725,27728],{"style":6783},[1889,27726],{"className":27727,"style":6746},[2092],[1889,27729],{"className":27730,"style":6791},[6790],[1889,27732,27733,27736],{"style":6794},[1889,27734],{"className":27735,"style":6746},[2092],[1889,27737,27739,27742,27745,27748,27751],{"className":27738},[1932],[1889,27740,24658],{"className":27741},[1932],[1889,27743],{"className":27744,"style":4041},[2042],[1889,27746,3917],{"className":27747},[4045],[1889,27749],{"className":27750,"style":4041},[2042],[1889,27752,27530],{"className":27753},[1932],[1889,27755,2108],{"className":27756},[2107],[1889,27758,27760],{"className":27759},[2080],[1889,27761,27763],{"className":27762,"style":6813},[2084],[1889,27764],{},[1889,27766],{"className":27767},[2367,6726],[1889,27769],{"className":27770,"style":2043},[2042],[1889,27772,1957],{"className":27773},[2047],[1889,27775],{"className":27776,"style":2043},[2042],[1889,27778,27780,27783],{"className":27779},[1923],[1889,27781],{"className":27782,"style":2694},[1927],[1889,27784,27537],{"className":27785},[1932],[1798,27787,27788,27789,27817,27818,27869,27870,27952],{},"但",[1889,27790,27792,27805],{"className":27791},[1892],[1889,27793,27795],{"className":27794},[1896],[1898,27796,27797],{"xmlns":1900},[1902,27798,27799,27803],{},[1905,27800,27801],{},[1908,27802,1967],{},[1912,27804,1967],{"encoding":1914},[1889,27806,27808],{"className":27807,"ariaHidden":1919},[1918],[1889,27809,27811,27814],{"className":27810},[1923],[1889,27812],{"className":27813,"style":5332},[1927],[1889,27815,1967],{"className":27816},[1932,1933],"不能超过",[1889,27819,27821,27839],{"className":27820},[1892],[1889,27822,27824],{"className":27823},[1896],[1898,27825,27826],{"xmlns":1900},[1902,27827,27828,27836],{},[1905,27829,27830,27832,27834],{},[1908,27831,1910],{},[1955,27833,1957],{},[1969,27835,25397],{},[1912,27837,27838],{"encoding":1914},"L=400",[1889,27840,27842,27860],{"className":27841,"ariaHidden":1919},[1918],[1889,27843,27845,27848,27851,27854,27857],{"className":27844},[1923],[1889,27846],{"className":27847,"style":1928},[1927],[1889,27849,1910],{"className":27850},[1932,1933],[1889,27852],{"className":27853,"style":2043},[2042],[1889,27855,1957],{"className":27856},[2047],[1889,27858],{"className":27859,"style":2043},[2042],[1889,27861,27863,27866],{"className":27862},[1923],[1889,27864],{"className":27865,"style":2694},[1927],[1889,27867,25397],{"className":27868},[1932],"，所以检查边界：实际上在内部解，",[1889,27871,27873,27896],{"className":27872},[1892],[1889,27874,27876],{"className":27875},[1896],[1898,27877,27878],{"xmlns":1900},[1902,27879,27880,27893],{},[1905,27881,27882,27888,27890],{},[2783,27883,27884,27886],{},[1908,27885,1967],{},[1955,27887,15587],{},[1955,27889,7183],{},[1969,27891,27892],{},"323",[1912,27894,27895],{"encoding":1914},"x^* \\approx 323",[1889,27897,27899,27943],{"className":27898,"ariaHidden":1919},[1918],[1889,27900,27902,27905,27934,27937,27940],{"className":27901},[1923],[1889,27903],{"className":27904,"style":15604},[1927],[1889,27906,27908,27911],{"className":27907},[1932],[1889,27909,1967],{"className":27910},[1932,1933],[1889,27912,27914],{"className":27913},[2071],[1889,27915,27917],{"className":27916},[2075],[1889,27918,27920],{"className":27919},[2080],[1889,27921,27923],{"className":27922,"style":15604},[2084],[1889,27924,27925,27928],{"style":2825},[1889,27926],{"className":27927,"style":2093},[2092],[1889,27929,27931],{"className":27930},[2097,2098,2099,2100],[1889,27932,15587],{"className":27933},[4045,2100],[1889,27935],{"className":27936,"style":2043},[2042],[1889,27938,7183],{"className":27939},[2047],[1889,27941],{"className":27942,"style":2043},[2042],[1889,27944,27946,27949],{"className":27945},[1923],[1889,27947],{"className":27948,"style":2694},[1927],[1889,27950,27892],{"className":27951},[1932],"（需要数值求解精确值）。",[1870,27954],{},[1794,27956,27958],{"id":27957},"_7-应用案例","7. 应用案例",[1877,27960,27962],{"id":27961},"_71-金融市场中的风险溢价","7.1 金融市场中的风险溢价",[1798,27964,27965,2704],{},[1884,27966,27967],{},"股权风险溢价之谜 (Equity Premium Puzzle)",[1798,27969,27970,27971,28044],{},"历史数据显示股票收益率比国债高约6-8个百分点（年化），但用标准的CRRA效用（",[1889,27972,27974,27996],{"className":27973},[1892],[1889,27975,27977],{"className":27976},[1896],[1898,27978,27979],{"xmlns":1900},[1902,27980,27981,27993],{},[1905,27982,27983,27985,27987,27989,27991],{},[1908,27984,11329],{},[1955,27986,7183],{},[1969,27988,1971],{},[1955,27990,3917],{},[1969,27992,1990],{},[1912,27994,27995],{"encoding":1914},"\\gamma \\approx 1-2",[1889,27997,27999,28017,28035],{"className":27998,"ariaHidden":1919},[1918],[1889,28000,28002,28005,28008,28011,28014],{"className":28001},[1923],[1889,28003],{"className":28004,"style":23166},[1927],[1889,28006,11329],{"className":28007,"style":11391},[1932,1933],[1889,28009],{"className":28010,"style":2043},[2042],[1889,28012,7183],{"className":28013},[2047],[1889,28015],{"className":28016,"style":2043},[2042],[1889,28018,28020,28023,28026,28029,28032],{"className":28019},[1923],[1889,28021],{"className":28022,"style":12913},[1927],[1889,28024,1971],{"className":28025},[1932],[1889,28027],{"className":28028,"style":4041},[2042],[1889,28030,3917],{"className":28031},[4045],[1889,28033],{"className":28034,"style":4041},[2042],[1889,28036,28038,28041],{"className":28037},[1923],[1889,28039],{"className":28040,"style":2694},[1927],[1889,28042,1990],{"className":28043},[1932],"）无法解释如此高的溢价。",[1798,28046,28047,2704],{},[1884,28048,28049],{},"可能解释",[6182,28051,28052,28107,28110,28113],{},[1808,28053,28054,28055,15854],{},"更高的风险规避系数（",[1889,28056,28058,28077],{"className":28057},[1892],[1889,28059,28061],{"className":28060},[1896],[1898,28062,28063],{"xmlns":1900},[1902,28064,28065,28074],{},[1905,28066,28067,28069,28071],{},[1908,28068,11329],{},[1955,28070,6369],{},[1969,28072,28073],{},"5",[1912,28075,28076],{"encoding":1914},"\\gamma > 5",[1889,28078,28080,28098],{"className":28079,"ariaHidden":1919},[1918],[1889,28081,28083,28086,28089,28092,28095],{"className":28082},[1923],[1889,28084],{"className":28085,"style":19092},[1927],[1889,28087,11329],{"className":28088,"style":11391},[1932,1933],[1889,28090],{"className":28091,"style":2043},[2042],[1889,28093,6369],{"className":28094},[2047],[1889,28096],{"className":28097,"style":2043},[2042],[1889,28099,28101,28104],{"className":28100},[1923],[1889,28102],{"className":28103,"style":2694},[1927],[1889,28105,28073],{"className":28106},[1932],[1808,28108,28109],{},"损失规避（前景理论）",[1808,28111,28112],{},"流动性约束",[1808,28114,28115],{},"罕见灾难风险",[1877,28117,28119],{"id":28118},"_72-健康保险的逆向选择","7.2 健康保险的逆向选择",[1798,28121,28122],{},"为什么健康的人不愿意购买健康保险？",[1798,28124,28125,28128,28129,2704],{},[1884,28126,28127],{},"传统解释",": 期望成本低，保费相对较高\n",[1884,28130,28131],{},"行为解释",[1805,28133,28134,28137,28140],{},[1808,28135,28136],{},"过度自信（低估自己生病概率）",[1808,28138,28139],{},"当前偏见（未来健康问题被过度折现）",[1808,28141,28142],{},"损失规避（保费是确定损失，疾病是不确定损失）",[1870,28144],{},[1794,28146,28148],{"id":28147},"_8-文献与拓展","8. 文献与拓展",[1798,28150,28151,2704],{},[1884,28152,28153],{},"经典论文",[1805,28155,28156,28163,28166,28169],{},[1808,28157,28158,28159],{},"von Neumann & Morgenstern (1944). ",[28160,28161,28162],"em",{},"Theory of Games and Economic Behavior",[1808,28164,28165],{},"Arrow, K. (1971). \"Essays in the Theory of Risk-Bearing\"",[1808,28167,28168],{},"Pratt, J. (1964). \"Risk Aversion in the Small and in the Large\"",[1808,28170,28171],{},"Kahneman & Tversky (1979). \"Prospect Theory: An Analysis of Decision under Risk\"",[1798,28173,28174,2704],{},[1884,28175,28176],{},"现代教材",[1805,28178,28179,28182,28185],{},[1808,28180,28181],{},"Mas-Colell et al. (1995), Chapter 6",[1808,28183,28184],{},"Jehle & Reny (2011), Chapter 4",[1808,28186,28187,28188],{},"Kreps (1988). ",[28160,28189,28190],{},"Notes on the Theory of Choice",[1870,28192],{},[1794,28194,28196],{"id":28195},"_9-本章小结","9. 本章小结",[10841,28198,28199,28212],{},[10844,28200,28201],{},[10847,28202,28203,28206,28209],{},[10850,28204,28205],{},"核心概念",[10850,28207,28208],{},"关键结果",[10850,28210,28211],{},"应用",[10994,28213,28214,28401,28514,28676,28769],{},[10847,28215,28216,28220,28398],{},[10999,28217,28218],{},[1884,28219,6189],{},[10999,28221,28222],{},[1889,28223,28225,28267],{"className":28224},[1892],[1889,28226,28228],{"className":28227},[1896],[1898,28229,28230],{"xmlns":1900},[1902,28231,28232,28264],{},[1905,28233,28234,28236,28238,28240,28242,28244,28246,28252,28254,28256,28262],{},[1908,28235,5673],{},[1955,28237,1961],{"stretchy":1960},[1908,28239,1910],{},[1955,28241,2023],{"stretchy":1960},[1955,28243,1957],{},[1955,28245,2534],{},[1963,28247,28248,28250],{},[1908,28249,1798],{},[1908,28251,2389],{},[1908,28253,5308],{},[1955,28255,1961],{"stretchy":1960},[1963,28257,28258,28260],{},[1908,28259,1967],{},[1908,28261,2389],{},[1955,28263,2023],{"stretchy":1960},[1912,28265,28266],{"encoding":1914},"U(L) = \\sum p_i u(x_i)",[1889,28268,28270,28297],{"className":28269,"ariaHidden":1919},[1918],[1889,28271,28273,28276,28279,28282,28285,28288,28291,28294],{"className":28272},[1923],[1889,28274],{"className":28275,"style":2057},[1927],[1889,28277,5673],{"className":28278,"style":5749},[1932,1933],[1889,28280,1961],{"className":28281},[2061],[1889,28283,1910],{"className":28284},[1932,1933],[1889,28286,2023],{"className":28287},[2367],[1889,28289],{"className":28290,"style":2043},[2042],[1889,28292,1957],{"className":28293},[2047],[1889,28295],{"className":28296,"style":2043},[2042],[1889,28298,28300,28303,28306,28309,28349,28352,28355,28395],{"className":28299},[1923],[1889,28301],{"className":28302,"style":2057},[1927],[1889,28304,2534],{"className":28305,"style":2577},[2571,2575,2576],[1889,28307],{"className":28308,"style":2125},[2042],[1889,28310,28312,28315],{"className":28311},[1932],[1889,28313,1798],{"className":28314},[1932,1933],[1889,28316,28318],{"className":28317},[2071],[1889,28319,28321,28341],{"className":28320},[2075,2076],[1889,28322,28324,28338],{"className":28323},[2080],[1889,28325,28327],{"className":28326,"style":2421},[2084],[1889,28328,28329,28332],{"style":2088},[1889,28330],{"className":28331,"style":2093},[2092],[1889,28333,28335],{"className":28334},[2097,2098,2099,2100],[1889,28336,2389],{"className":28337},[1932,1933,2100],[1889,28339,2108],{"className":28340},[2107],[1889,28342,28344],{"className":28343},[2080],[1889,28345,28347],{"className":28346,"style":2115},[2084],[1889,28348],{},[1889,28350,5308],{"className":28351},[1932,1933],[1889,28353,1961],{"className":28354},[2061],[1889,28356,28358,28361],{"className":28357},[1932],[1889,28359,1967],{"className":28360},[1932,1933],[1889,28362,28364],{"className":28363},[2071],[1889,28365,28367,28387],{"className":28366},[2075,2076],[1889,28368,28370,28384],{"className":28369},[2080],[1889,28371,28373],{"className":28372,"style":2421},[2084],[1889,28374,28375,28378],{"style":2088},[1889,28376],{"className":28377,"style":2093},[2092],[1889,28379,28381],{"className":28380},[2097,2098,2099,2100],[1889,28382,2389],{"className":28383},[1932,1933,2100],[1889,28385,2108],{"className":28386},[2107],[1889,28388,28390],{"className":28389},[2080],[1889,28391,28393],{"className":28392,"style":2115},[2084],[1889,28394],{},[1889,28396,2023],{"className":28397},[2367],[10999,28399,28400],{},"决策规则",[10847,28402,28403,28407,28511],{},[10999,28404,28405],{},[1884,28406,23228],{},[10999,28408,28409],{},[1889,28410,28412,28443],{"className":28411},[1892],[1889,28413,28415],{"className":28414},[1896],[1898,28416,28417],{"xmlns":1900},[1902,28418,28419,28441],{},[1905,28420,28421,28431,28433,28435,28437,28439],{},[2783,28422,28423,28425],{},[1908,28424,5308],{},[1905,28426,28427,28429],{},[1955,28428,2791],{"mathvariant":2789},[1955,28430,2791],{"mathvariant":2789},[1955,28432,1961],{"stretchy":1960},[1908,28434,8472],{},[1955,28436,2023],{"stretchy":1960},[1955,28438,8012],{},[1969,28440,3819],{},[1912,28442,9293],{"encoding":1914},[1889,28444,28446,28502],{"className":28445,"ariaHidden":1919},[1918],[1889,28447,28449,28452,28484,28487,28490,28493,28496,28499],{"className":28448},[1923],[1889,28450],{"className":28451,"style":6134},[1927],[1889,28453,28455,28458],{"className":28454},[1932],[1889,28456,5308],{"className":28457},[1932,1933],[1889,28459,28461],{"className":28460},[2071],[1889,28462,28464],{"className":28463},[2075],[1889,28465,28467],{"className":28466},[2080],[1889,28468,28470],{"className":28469,"style":2804},[2084],[1889,28471,28472,28475],{"style":2825},[1889,28473],{"className":28474,"style":2093},[2092],[1889,28476,28478],{"className":28477},[2097,2098,2099,2100],[1889,28479,28481],{"className":28480},[1932,2100],[1889,28482,8176],{"className":28483},[1932,2100],[1889,28485,1961],{"className":28486},[2061],[1889,28488,8472],{"className":28489,"style":8687},[1932,1933],[1889,28491,2023],{"className":28492},[2367],[1889,28494],{"className":28495,"style":2043},[2042],[1889,28497,8012],{"className":28498},[2047],[1889,28500],{"className":28501,"style":2043},[2042],[1889,28503,28505,28508],{"className":28504},[1923],[1889,28506],{"className":28507,"style":2694},[1927],[1889,28509,3819],{"className":28510},[1932],[10999,28512,28513],{},"保险需求",[10847,28515,28516,28521,28674],{},[10999,28517,28518],{},[1884,28519,28520],{},"ARA\u002FRRA",[10999,28522,28523],{},[1889,28524,28526,28568],{"className":28525},[1892],[1889,28527,28529],{"className":28528},[1896],[1898,28530,28531],{"xmlns":1900},[1902,28532,28533,28565],{},[1905,28534,28535,28537,28539,28541,28543,28545,28547,28557,28559],{},[1908,28536,9839],{},[1955,28538,1961],{"stretchy":1960},[1908,28540,8472],{},[1955,28542,2023],{"stretchy":1960},[1955,28544,1957],{},[1955,28546,3917],{},[2783,28548,28549,28551],{},[1908,28550,5308],{},[1905,28552,28553,28555],{},[1955,28554,2791],{"mathvariant":2789},[1955,28556,2791],{"mathvariant":2789},[1908,28558,11106],{"mathvariant":2789},[2783,28560,28561,28563],{},[1908,28562,5308],{},[1955,28564,2791],{"mathvariant":2789,"lspace":2790,"rspace":2790},[1912,28566,28567],{"encoding":1914},"A(w) = -u''\u002Fu'",[1889,28569,28571,28598],{"className":28570,"ariaHidden":1919},[1918],[1889,28572,28574,28577,28580,28583,28586,28589,28592,28595],{"className":28573},[1923],[1889,28575],{"className":28576,"style":2057},[1927],[1889,28578,9839],{"className":28579},[1932,1933],[1889,28581,1961],{"className":28582},[2061],[1889,28584,8472],{"className":28585,"style":8687},[1932,1933],[1889,28587,2023],{"className":28588},[2367],[1889,28590],{"className":28591,"style":2043},[2042],[1889,28593,1957],{"className":28594},[2047],[1889,28596],{"className":28597,"style":2043},[2042],[1889,28599,28601,28604,28607,28639,28642],{"className":28600},[1923],[1889,28602],{"className":28603,"style":6134},[1927],[1889,28605,3917],{"className":28606},[1932],[1889,28608,28610,28613],{"className":28609},[1932],[1889,28611,5308],{"className":28612},[1932,1933],[1889,28614,28616],{"className":28615},[2071],[1889,28617,28619],{"className":28618},[2075],[1889,28620,28622],{"className":28621},[2080],[1889,28623,28625],{"className":28624,"style":2804},[2084],[1889,28626,28627,28630],{"style":2825},[1889,28628],{"className":28629,"style":2093},[2092],[1889,28631,28633],{"className":28632},[2097,2098,2099,2100],[1889,28634,28636],{"className":28635},[1932,2100],[1889,28637,8176],{"className":28638},[1932,2100],[1889,28640,11106],{"className":28641},[1932],[1889,28643,28645,28648],{"className":28644},[1932],[1889,28646,5308],{"className":28647},[1932,1933],[1889,28649,28651],{"className":28650},[2071],[1889,28652,28654],{"className":28653},[2075],[1889,28655,28657],{"className":28656},[2080],[1889,28658,28660],{"className":28659,"style":2804},[2084],[1889,28661,28662,28665],{"style":2825},[1889,28663],{"className":28664,"style":2093},[2092],[1889,28666,28668],{"className":28667},[2097,2098,2099,2100],[1889,28669,28671],{"className":28670},[1932,2100],[1889,28672,2791],{"className":28673},[1932,2100],[10999,28675,20884],{},[10847,28677,28678,28682,28766],{},[10999,28679,28680],{},[1884,28681,15568],{},[10999,28683,28684,28685],{},"公平保费下",[1889,28686,28688,28710],{"className":28687},[1892],[1889,28689,28691],{"className":28690},[1896],[1898,28692,28693],{"xmlns":1900},[1902,28694,28695,28707],{},[1905,28696,28697,28703,28705],{},[2783,28698,28699,28701],{},[1908,28700,1967],{},[1955,28702,15587],{},[1955,28704,1957],{},[1908,28706,1910],{},[1912,28708,28709],{"encoding":1914},"x^*=L",[1889,28711,28713,28757],{"className":28712,"ariaHidden":1919},[1918],[1889,28714,28716,28719,28748,28751,28754],{"className":28715},[1923],[1889,28717],{"className":28718,"style":15604},[1927],[1889,28720,28722,28725],{"className":28721},[1932],[1889,28723,1967],{"className":28724},[1932,1933],[1889,28726,28728],{"className":28727},[2071],[1889,28729,28731],{"className":28730},[2075],[1889,28732,28734],{"className":28733},[2080],[1889,28735,28737],{"className":28736,"style":15604},[2084],[1889,28738,28739,28742],{"style":2825},[1889,28740],{"className":28741,"style":2093},[2092],[1889,28743,28745],{"className":28744},[2097,2098,2099,2100],[1889,28746,15587],{"className":28747},[4045,2100],[1889,28749],{"className":28750,"style":2043},[2042],[1889,28752,1957],{"className":28753},[2047],[1889,28755],{"className":28756,"style":2043},[2042],[1889,28758,28760,28763],{"className":28759},[1923],[1889,28761],{"className":28762,"style":1928},[1927],[1889,28764,1910],{"className":28765},[1932,1933],[10999,28767,28768],{},"保险市场",[10847,28770,28771,28776,28779],{},[10999,28772,28773],{},[1884,28774,28775],{},"前景理论",[10999,28777,28778],{},"损失规避+概率权重",[10999,28780,28781],{},"行为金融",[1798,28783,28784,28786,28787,28789,28790,28792,28793,28795],{},[1884,28785,6180],{},":\n✅ 理性决策者最大化期望效用，而非期望价值",[22646,28788],{},"\n✅ 风险规避源于边际效用递减",[22646,28791],{},"\n✅ 公平保险下会完全保险",[22646,28794],{},"\n✅ 真实决策系统性偏离期望效用理论预测",[1794,28797,28798],{"id":28798},"自学检查",[1798,28800,28801,28804],{},[1884,28802,28803],{},"核心直觉回看","：不确定性下的选择不是比较“平均收益”这么简单。风险规避者关心的是财富状态上的效用平均值，而不是财富本身的平均值；凹效用函数让坏状态的损失权重更重。",[1798,28806,28807,28810,28811,28967],{},[1884,28808,28809],{},"关键模型提醒","：彩票 ",[1889,28812,28814,28848],{"className":28813},[1892],[1889,28815,28817],{"className":28816},[1896],[1898,28818,28819],{"xmlns":1900},[1902,28820,28821,28845],{},[1905,28822,28823,28825,28827,28829,28835,28837,28843],{},[1908,28824,1910],{},[1955,28826,1957],{},[1955,28828,1961],{"stretchy":1960},[1963,28830,28831,28833],{},[1908,28832,1798],{},[1908,28834,2389],{},[1955,28836,1974],{"separator":1919},[1963,28838,28839,28841],{},[1908,28840,8472],{},[1908,28842,2389],{},[1955,28844,2023],{"stretchy":1960},[1912,28846,28847],{"encoding":1914},"L=(p_i,w_i)",[1889,28849,28851,28869],{"className":28850,"ariaHidden":1919},[1918],[1889,28852,28854,28857,28860,28863,28866],{"className":28853},[1923],[1889,28855],{"className":28856,"style":1928},[1927],[1889,28858,1910],{"className":28859},[1932,1933],[1889,28861],{"className":28862,"style":2043},[2042],[1889,28864,1957],{"className":28865},[2047],[1889,28867],{"className":28868,"style":2043},[2042],[1889,28870,28872,28875,28878,28918,28921,28924,28964],{"className":28871},[1923],[1889,28873],{"className":28874,"style":2057},[1927],[1889,28876,1961],{"className":28877},[2061],[1889,28879,28881,28884],{"className":28880},[1932],[1889,28882,1798],{"className":28883},[1932,1933],[1889,28885,28887],{"className":28886},[2071],[1889,28888,28890,28910],{"className":28889},[2075,2076],[1889,28891,28893,28907],{"className":28892},[2080],[1889,28894,28896],{"className":28895,"style":2421},[2084],[1889,28897,28898,28901],{"style":2088},[1889,28899],{"className":28900,"style":2093},[2092],[1889,28902,28904],{"className":28903},[2097,2098,2099,2100],[1889,28905,2389],{"className":28906},[1932,1933,2100],[1889,28908,2108],{"className":28909},[2107],[1889,28911,28913],{"className":28912},[2080],[1889,28914,28916],{"className":28915,"style":2115},[2084],[1889,28917],{},[1889,28919,1974],{"className":28920},[2121],[1889,28922],{"className":28923,"style":2125},[2042],[1889,28925,28927,28930],{"className":28926},[1932],[1889,28928,8472],{"className":28929,"style":8687},[1932,1933],[1889,28931,28933],{"className":28932},[2071],[1889,28934,28936,28956],{"className":28935},[2075,2076],[1889,28937,28939,28953],{"className":28938},[2080],[1889,28940,28942],{"className":28941,"style":2421},[2084],[1889,28943,28944,28947],{"style":12188},[1889,28945],{"className":28946,"style":2093},[2092],[1889,28948,28950],{"className":28949},[2097,2098,2099,2100],[1889,28951,2389],{"className":28952},[1932,1933,2100],[1889,28954,2108],{"className":28955},[2107],[1889,28957,28959],{"className":28958},[2080],[1889,28960,28962],{"className":28961,"style":2115},[2084],[1889,28963],{},[1889,28965,2023],{"className":28966},[2367]," 的期望效用为",[1889,28969,28971],{"className":28970},[1938],[1889,28972,28974,29025],{"className":28973},[1892],[1889,28975,28977],{"className":28976},[1896],[1898,28978,28979],{"xmlns":1900,"display":1947},[1902,28980,28981,29022],{},[1905,28982,28983,28985,28987,28989,28991,28993,28995,29001,29007,29009,29011,29017,29019],{},[1908,28984,5719],{},[1908,28986,5673],{},[1955,28988,1961],{"stretchy":1960},[1908,28990,1910],{},[1955,28992,2023],{"stretchy":1960},[1955,28994,1957],{},[13372,28996,28997,28999],{},[1955,28998,2534],{},[1908,29000,2389],{},[1963,29002,29003,29005],{},[1908,29004,1798],{},[1908,29006,2389],{},[1908,29008,5308],{},[1955,29010,1961],{"stretchy":1960},[1963,29012,29013,29015],{},[1908,29014,8472],{},[1908,29016,2389],{},[1955,29018,2023],{"stretchy":1960},[1908,29020,29021],{"mathvariant":2789},".",[1912,29023,29024],{"encoding":1914},"EU(L)=\\sum_i p_i u(w_i).",[1889,29026,29028,29058],{"className":29027,"ariaHidden":1919},[1918],[1889,29029,29031,29034,29037,29040,29043,29046,29049,29052,29055],{"className":29030},[1923],[1889,29032],{"className":29033,"style":2057},[1927],[1889,29035,5719],{"className":29036,"style":9591},[1932,1933],[1889,29038,5673],{"className":29039,"style":5749},[1932,1933],[1889,29041,1961],{"className":29042},[2061],[1889,29044,1910],{"className":29045},[1932,1933],[1889,29047,2023],{"className":29048},[2367],[1889,29050],{"className":29051,"style":2043},[2042],[1889,29053,1957],{"className":29054},[2047],[1889,29056],{"className":29057,"style":2043},[2042],[1889,29059,29061,29065,29110,29113,29153,29156,29159,29199,29202],{"className":29060},[1923],[1889,29062],{"className":29063,"style":29064},[1927],"height:2.3277em;vertical-align:-1.2777em;",[1889,29066,29068],{"className":29067},[2571,5778],[1889,29069,29071,29102],{"className":29070},[2075,2076],[1889,29072,29074,29099],{"className":29073},[2080],[1889,29075,29078,29089],{"className":29076,"style":29077},[2084],"height:1.05em;",[1889,29079,29080,29083],{"style":5791},[1889,29081],{"className":29082,"style":5795},[2092],[1889,29084,29086],{"className":29085},[2097,2098,2099,2100],[1889,29087,2389],{"className":29088},[1932,1933,2100],[1889,29090,29091,29094],{"style":5813},[1889,29092],{"className":29093,"style":5795},[2092],[1889,29095,29096],{},[1889,29097,2534],{"className":29098},[2571,2575,5822],[1889,29100,2108],{"className":29101},[2107],[1889,29103,29105],{"className":29104},[2080],[1889,29106,29108],{"className":29107,"style":5844},[2084],[1889,29109],{},[1889,29111],{"className":29112,"style":2125},[2042],[1889,29114,29116,29119],{"className":29115},[1932],[1889,29117,1798],{"className":29118},[1932,1933],[1889,29120,29122],{"className":29121},[2071],[1889,29123,29125,29145],{"className":29124},[2075,2076],[1889,29126,29128,29142],{"className":29127},[2080],[1889,29129,29131],{"className":29130,"style":2421},[2084],[1889,29132,29133,29136],{"style":2088},[1889,29134],{"className":29135,"style":2093},[2092],[1889,29137,29139],{"className":29138},[2097,2098,2099,2100],[1889,29140,2389],{"className":29141},[1932,1933,2100],[1889,29143,2108],{"className":29144},[2107],[1889,29146,29148],{"className":29147},[2080],[1889,29149,29151],{"className":29150,"style":2115},[2084],[1889,29152],{},[1889,29154,5308],{"className":29155},[1932,1933],[1889,29157,1961],{"className":29158},[2061],[1889,29160,29162,29165],{"className":29161},[1932],[1889,29163,8472],{"className":29164,"style":8687},[1932,1933],[1889,29166,29168],{"className":29167},[2071],[1889,29169,29171,29191],{"className":29170},[2075,2076],[1889,29172,29174,29188],{"className":29173},[2080],[1889,29175,29177],{"className":29176,"style":2421},[2084],[1889,29178,29179,29182],{"style":12188},[1889,29180],{"className":29181,"style":2093},[2092],[1889,29183,29185],{"className":29184},[2097,2098,2099,2100],[1889,29186,2389],{"className":29187},[1932,1933,2100],[1889,29189,2108],{"className":29190},[2107],[1889,29192,29194],{"className":29193},[2080],[1889,29195,29197],{"className":29196,"style":2115},[2084],[1889,29198],{},[1889,29200,2023],{"className":29201},[2367],[1889,29203,29021],{"className":29204},[1932],[1798,29206,29207,29208,29306],{},"风险溢价来自 ",[1889,29209,29211,29249],{"className":29210},[1892],[1889,29212,29214],{"className":29213},[1896],[1898,29215,29216],{"xmlns":1900},[1902,29217,29218,29246],{},[1905,29219,29220,29222,29224,29226,29228,29230,29232,29234,29236,29238,29240,29242,29244],{},[1908,29221,5308],{},[1955,29223,1961],{"stretchy":1960},[1908,29225,5719],{},[1908,29227,8472],{},[1955,29229,2023],{"stretchy":1960},[1955,29231,3917],{},[1908,29233,5719],{},[1955,29235,5722],{"stretchy":1960},[1908,29237,5308],{},[1955,29239,1961],{"stretchy":1960},[1908,29241,8472],{},[1955,29243,2023],{"stretchy":1960},[1955,29245,5733],{"stretchy":1960},[1912,29247,29248],{"encoding":1914},"u(Ew)-E[u(w)]",[1889,29250,29252,29282],{"className":29251,"ariaHidden":1919},[1918],[1889,29253,29255,29258,29261,29264,29267,29270,29273,29276,29279],{"className":29254},[1923],[1889,29256],{"className":29257,"style":2057},[1927],[1889,29259,5308],{"className":29260},[1932,1933],[1889,29262,1961],{"className":29263},[2061],[1889,29265,5719],{"className":29266,"style":9591},[1932,1933],[1889,29268,8472],{"className":29269,"style":8687},[1932,1933],[1889,29271,2023],{"className":29272},[2367],[1889,29274],{"className":29275,"style":4041},[2042],[1889,29277,3917],{"className":29278},[4045],[1889,29280],{"className":29281,"style":4041},[2042],[1889,29283,29285,29288,29291,29294,29297,29300,29303],{"className":29284},[1923],[1889,29286],{"className":29287,"style":2057},[1927],[1889,29289,5719],{"className":29290,"style":9591},[1932,1933],[1889,29292,5722],{"className":29293},[2061],[1889,29295,5308],{"className":29296},[1932,1933],[1889,29298,1961],{"className":29299},[2061],[1889,29301,8472],{"className":29302,"style":8687},[1932,1933],[1889,29304,5972],{"className":29305},[2367]," 的差距；保险模型的核心是一阶条件把不同状态下的边际效用拉近。",[1877,29308,29309],{"id":29309},"常见误区",[1805,29311,29312,29315,29318,29321],{},[1808,29313,29314],{},"把期望效用最大化误写成期望财富最大化。风险中性时两者才一致。",[1808,29316,29317],{},"认为风险规避等于永远不冒险。只要风险补偿足够高，风险规避者也可能投资风险资产。",[1808,29319,29320],{},"看到公平保险就忘记“完全保险”依赖于凹效用、无交易成本和可验证损失。",[1808,29322,29323],{},"把前景理论理解成“人不理性所以无法建模”。它仍然是有结构的模型，只是参照点、损失规避和概率权重不同。",[1877,29325,29326],{"id":29326},"自测题",[6182,29328,29329,29445,29448,29451,29542],{},[1808,29330,29331,29332,29444],{},"对 ",[1889,29333,29335,29361],{"className":29334},[1892],[1889,29336,29338],{"className":29337},[1896],[1898,29339,29340],{"xmlns":1900},[1902,29341,29342,29358],{},[1905,29343,29344,29346,29348,29350,29352,29354],{},[1908,29345,5308],{},[1955,29347,1961],{"stretchy":1960},[1908,29349,8472],{},[1955,29351,2023],{"stretchy":1960},[1955,29353,1957],{},[23493,29355,29356],{},[1908,29357,8472],{},[1912,29359,29360],{"encoding":1914},"u(w)=\\sqrt{w}",[1889,29362,29364,29391],{"className":29363,"ariaHidden":1919},[1918],[1889,29365,29367,29370,29373,29376,29379,29382,29385,29388],{"className":29366},[1923],[1889,29368],{"className":29369,"style":2057},[1927],[1889,29371,5308],{"className":29372},[1932,1933],[1889,29374,1961],{"className":29375},[2061],[1889,29377,8472],{"className":29378,"style":8687},[1932,1933],[1889,29380,2023],{"className":29381},[2367],[1889,29383],{"className":29384,"style":2043},[2042],[1889,29386,1957],{"className":29387},[2047],[1889,29389],{"className":29390,"style":2043},[2042],[1889,29392,29394,29397],{"className":29393},[1923],[1889,29395],{"className":29396,"style":23536},[1927],[1889,29398,29400],{"className":29399},[1932,23540],[1889,29401,29403,29436],{"className":29402},[2075,2076],[1889,29404,29406,29433],{"className":29405},[2080],[1889,29407,29409,29421],{"className":29408,"style":23550},[2084],[1889,29410,29412,29415],{"className":29411,"style":8713},[23554],[1889,29413],{"className":29414,"style":6746},[2092],[1889,29416,29418],{"className":29417,"style":23561},[1932],[1889,29419,8472],{"className":29420,"style":8687},[1932,1933],[1889,29422,29423,29426],{"style":23567},[1889,29424],{"className":29425,"style":6746},[2092],[1889,29427,29429],{"className":29428,"style":23575},[23574],[23577,29430,29431],{"xmlns":23579,"width":23580,"height":23581,"viewBox":23582,"preserveAspectRatio":23583},[23585,29432],{"d":23587},[1889,29434,2108],{"className":29435},[2107],[1889,29437,29439],{"className":29438},[2080],[1889,29440,29442],{"className":29441,"style":23597},[2084],[1889,29443],{},"，比较确定得到 100 与一半概率得 64、一半概率得 144 的彩票。",[1808,29446,29447],{},"什么是确定性等价？它和风险溢价之间有什么关系？",[1808,29449,29450],{},"公平保费下，为什么风险规避者会选择完全保险？",[1808,29452,29453,29454,29497,29498,29541],{},"绝对风险规避系数 ",[1889,29455,29457,29476],{"className":29456},[1892],[1889,29458,29460],{"className":29459},[1896],[1898,29461,29462],{"xmlns":1900},[1902,29463,29464,29474],{},[1905,29465,29466,29468,29470,29472],{},[1908,29467,9839],{},[1955,29469,1961],{"stretchy":1960},[1908,29471,8472],{},[1955,29473,2023],{"stretchy":1960},[1912,29475,10729],{"encoding":1914},[1889,29477,29479],{"className":29478,"ariaHidden":1919},[1918],[1889,29480,29482,29485,29488,29491,29494],{"className":29481},[1923],[1889,29483],{"className":29484,"style":2057},[1927],[1889,29486,9839],{"className":29487},[1932,1933],[1889,29489,1961],{"className":29490},[2061],[1889,29492,8472],{"className":29493,"style":8687},[1932,1933],[1889,29495,2023],{"className":29496},[2367]," 和相对风险规避系数 ",[1889,29499,29501,29520],{"className":29500},[1892],[1889,29502,29504],{"className":29503},[1896],[1898,29505,29506],{"xmlns":1900},[1902,29507,29508,29518],{},[1905,29509,29510,29512,29514,29516],{},[1908,29511,5314],{},[1955,29513,1961],{"stretchy":1960},[1908,29515,8472],{},[1955,29517,2023],{"stretchy":1960},[1912,29519,10776],{"encoding":1914},[1889,29521,29523],{"className":29522,"ariaHidden":1919},[1918],[1889,29524,29526,29529,29532,29535,29538],{"className":29525},[1923],[1889,29527],{"className":29528,"style":2057},[1927],[1889,29530,5314],{"className":29531,"style":9718},[1932,1933],[1889,29533,1961],{"className":29534},[2061],[1889,29536,8472],{"className":29537,"style":8687},[1932,1933],[1889,29539,2023],{"className":29540},[2367]," 分别适合描述什么问题？",[1808,29543,29544],{},"前景理论如何解释人们在收益区间和损失区间的不同风险态度？",[1877,29546,29547],{"id":29547},"下一步学习提示",[1798,29549,29550],{},"把本章的“状态”思想带到一般均衡中：当存在多个商品、多个消费者和多个市场时，价格如何同时协调所有人的计划？下一章会把个体最优放进整个经济系统。",[1798,29552,29553,29556,29557,29560,29561,29564],{},[1884,29554,29555],{},"下一章预告",": 到目前为止，我们都假设只有一个决策者。但经济学的核心是研究",[1884,29558,29559],{},"互动"," —— 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