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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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Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",null,{"id":1784,"title":1260,"body":1785,"description":5837,"extension":5838,"features":1782,"hero":1782,"layout":1782,"locale":1782,"meta":5839,"navigation":1782,"path":1261,"published":5841,"seo":5842,"stem":1262,"__hash__":5843},"docs\u002Fzh\u002Fasset-pricing\u002F02-utility\u002Findex.md",{"type":1786,"value":1787,"toc":5816},"minimark",[1788,1792,1796,1799,1803,1863,1866,1869,1888,1891,1909,1912,1915,1918,1964,1967,2071,2137,2415,2418,2422,2425,2429,2732,3006,3009,3012,3015,3123,3126,3130,3133,3389,3392,3640,3733,3736,3776,3877,3880,3984,4055,4059,4194,4197,4361,4364,4536,4644,4704,4707,4811,4814,4818,4821,4827,4830,4833,4904,4907,5047,5050,5255,5258,5810,5813],[1789,1790,1260],"h1",{"id":1791},"第二章效用理论与风险偏好",[1793,1794,1795],"p",{},"第一章用现金流、贴现和无套利搭起了价格框架。本章回答更深一层的问题：为什么风险资产需要提供额外收益？为什么同样的赌博，有人愿意参与，有人宁愿买保险？资产定价中的“风险溢价”并不是凭空设定的参数，它来自投资者对不确定财富的偏好。",[1793,1797,1798],{},"效用理论的作用，是把“我不喜欢风险”翻译成可以推导、比较和估计的数学对象。你不需要把每个公理背成哲学命题，但要能看懂：凹效用意味着风险厌恶；风险厌恶程度决定确定性等价和风险溢价；这些概念会在均值-方差、CAPM 和跨期消费模型中反复出现。",[1800,1801,1802],"h2",{"id":1802},"本章路线",[1804,1805,1806,1819],"table",{},[1807,1808,1809],"thead",{},[1810,1811,1812,1816],"tr",{},[1813,1814,1815],"th",{},"课次",[1813,1817,1818],{},"核心问题",[1820,1821,1822,1831,1839,1847,1855],"tbody",{},[1810,1823,1824,1828],{},[1825,1826,1827],"td",{},"2.1 期望效用",[1825,1829,1830],{},"不确定财富怎样进入选择？",[1810,1832,1833,1836],{},[1825,1834,1835],{},"2.2 风险厌恶",[1825,1837,1838],{},"为什么同一风险对不同财富水平的人代价不同？",[1810,1840,1841,1844],{},[1825,1842,1843],{},"2.3 效用函数",[1825,1845,1846],{},"CARA、CRRA 与对数效用分别固定了什么？",[1810,1848,1849,1852],{},[1825,1850,1851],{},"2.4 随机占优",[1825,1853,1854],{},"不指定完整效用函数时还能排除哪些选择？",[1810,1856,1857,1860],{},[1825,1858,1859],{},"2.5 确定性等价",[1825,1861,1862],{},"投资者愿意用多少确定财富替代风险财富？",[1800,1864,1865],{"id":1865},"学习成果",[1793,1867,1868],{},"通过本章学习，你将掌握：",[1870,1871,1872,1876,1879,1882,1885],"ol",{},[1873,1874,1875],"li",{},"期望效用理论的公理化基础",[1873,1877,1878],{},"风险厌恶的度量方法",[1873,1880,1881],{},"不同效用函数的性质和应用",[1873,1883,1884],{},"随机占优的概念和判别方法",[1873,1886,1887],{},"确定性等价在资产定价中的应用",[1793,1889,1890],{},"读完本章后，你应能完成以下任务：",[1892,1893,1894,1897,1900,1903,1906],"ul",{},[1873,1895,1896],{},"判断一个效用函数是否体现风险厌恶、风险中性或风险偏好。",[1873,1898,1899],{},"用绝对风险厌恶和相对风险厌恶解释不同财富水平下的投资行为。",[1873,1901,1902],{},"计算简单彩票的期望效用、确定性等价和风险溢价。",[1873,1904,1905],{},"区分一阶随机占优与二阶随机占优，并说明它们为什么不依赖具体效用函数。",[1873,1907,1908],{},"解释为什么风险溢价取决于“坏状态下的损失”，而不只是收益率方差。",[1800,1910,1911],{"id":1911},"金融与经济动机",[1793,1913,1914],{},"在现实投资中，投资者并不是只最大化期望收益。一个 50% 概率赚 100 元、50% 概率亏 100 元的赌博，期望收益为 0，但大多数人不会无所谓；一个收益更高但在经济衰退时亏损更大的资产，也不一定比低收益的保险型资产更有吸引力。",[1793,1916,1917],{},"效用理论帮助我们把这些现象放进统一框架：",[1804,1919,1920,1930],{},[1807,1921,1922],{},[1810,1923,1924,1927],{},[1813,1925,1926],{},"现实问题",[1813,1928,1929],{},"效用理论中的表达",[1820,1931,1932,1940,1948,1956],{},[1810,1933,1934,1937],{},[1825,1935,1936],{},"为什么人们买保险",[1825,1938,1939],{},"愿意牺牲一部分期望财富，换取更稳定的财富",[1810,1941,1942,1945],{},[1825,1943,1944],{},"为什么股票要有风险溢价",[1825,1946,1947],{},"股票在坏状态亏损，需要补偿风险厌恶投资者",[1810,1949,1950,1953],{},[1825,1951,1952],{},"为什么富人和普通人的风险承受能力不同",[1825,1954,1955],{},"风险厌恶可能随财富变化",[1810,1957,1958,1961],{},[1825,1959,1960],{},"为什么“高期望收益”不等于“更优选择”",[1825,1962,1963],{},"需要比较期望效用而非期望金额",[1800,1965,1966],{"id":1966},"模型设置与直觉",[1793,1968,1969,1970,2017,2018,2070],{},"设投资者最终财富为随机变量 ",[1971,1972,1975,1997],"span",{"className":1973},[1974],"katex",[1971,1976,1979],{"className":1977},[1978],"katex-mathml",[1980,1981,1983],"math",{"xmlns":1982},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1984,1985,1986,1993],"semantics",{},[1987,1988,1989],"mrow",{},[1990,1991,1992],"mi",{},"W",[1994,1995,1992],"annotation",{"encoding":1996},"application\u002Fx-tex",[1971,1998,2002],{"className":1999,"ariaHidden":2001},[2000],"katex-html","true",[1971,2003,2006,2011],{"className":2004},[2005],"base",[1971,2007],{"className":2008,"style":2010},[2009],"strut","height:0.6833em;",[1971,2012,1992],{"className":2013,"style":2016},[2014,2015],"mord","mathnormal","margin-right:0.1389em;","，效用函数为 ",[1971,2019,2021,2046],{"className":2020},[1974],[1971,2022,2024],{"className":2023},[1978],[1980,2025,2026],{"xmlns":1982},[1984,2027,2028,2043],{},[1987,2029,2030,2033,2038,2040],{},[1990,2031,2032],{},"u",[2034,2035,2037],"mo",{"stretchy":2036},"false","(",[1990,2039,1992],{},[2034,2041,2042],{"stretchy":2036},")",[1994,2044,2045],{"encoding":1996},"u(W)",[1971,2047,2049],{"className":2048,"ariaHidden":2001},[2000],[1971,2050,2052,2056,2059,2063,2066],{"className":2051},[2005],[1971,2053],{"className":2054,"style":2055},[2009],"height:1em;vertical-align:-0.25em;",[1971,2057,2032],{"className":2058},[2014,2015],[1971,2060,2037],{"className":2061},[2062],"mopen",[1971,2064,1992],{"className":2065,"style":2016},[2014,2015],[1971,2067,2042],{"className":2068},[2069],"mclose","。在期望效用框架下，投资者比较不同选择时看的是：",[1971,2072,2075],{"className":2073},[2074],"katex-display",[1971,2076,2078,2108],{"className":2077},[1974],[1971,2079,2081],{"className":2080},[1978],[1980,2082,2084],{"xmlns":1982,"display":2083},"block",[1984,2085,2086,2105],{},[1987,2087,2088,2091,2094,2096,2098,2100,2102],{},[1990,2089,2090],{},"E",[2034,2092,2093],{"stretchy":2036},"[",[1990,2095,2032],{},[2034,2097,2037],{"stretchy":2036},[1990,2099,1992],{},[2034,2101,2042],{"stretchy":2036},[2034,2103,2104],{"stretchy":2036},"]",[1994,2106,2107],{"encoding":1996},"E[u(W)]",[1971,2109,2111],{"className":2110,"ariaHidden":2001},[2000],[1971,2112,2114,2117,2121,2124,2127,2130,2133],{"className":2113},[2005],[1971,2115],{"className":2116,"style":2055},[2009],[1971,2118,2090],{"className":2119,"style":2120},[2014,2015],"margin-right:0.0576em;",[1971,2122,2093],{"className":2123},[2062],[1971,2125,2032],{"className":2126},[2014,2015],[1971,2128,2037],{"className":2129},[2062],[1971,2131,1992],{"className":2132,"style":2016},[2014,2015],[1971,2134,2136],{"className":2135},[2069],")]",[1793,2138,2139,2140,2184,2185,2308,2309,2414],{},"而不是 ",[1971,2141,2143,2163],{"className":2142},[1974],[1971,2144,2146],{"className":2145},[1978],[1980,2147,2148],{"xmlns":1982},[1984,2149,2150,2160],{},[1987,2151,2152,2154,2156,2158],{},[1990,2153,2090],{},[2034,2155,2093],{"stretchy":2036},[1990,2157,1992],{},[2034,2159,2104],{"stretchy":2036},[1994,2161,2162],{"encoding":1996},"E[W]",[1971,2164,2166],{"className":2165,"ariaHidden":2001},[2000],[1971,2167,2169,2172,2175,2178,2181],{"className":2168},[2005],[1971,2170],{"className":2171,"style":2055},[2009],[1971,2173,2090],{"className":2174,"style":2120},[2014,2015],[1971,2176,2093],{"className":2177},[2062],[1971,2179,1992],{"className":2180,"style":2016},[2014,2015],[1971,2182,2104],{"className":2183},[2069],"。若 ",[1971,2186,2188,2223],{"className":2187},[1974],[1971,2189,2191],{"className":2190},[1978],[1980,2192,2193],{"xmlns":1982},[1984,2194,2195,2220],{},[1987,2196,2197,2207,2209,2211,2213,2216],{},[2198,2199,2200,2202],"msup",{},[1990,2201,2032],{},[2034,2203,2206],{"mathvariant":2204,"lspace":2205,"rspace":2205},"normal","0em","′",[2034,2208,2037],{"stretchy":2036},[1990,2210,1992],{},[2034,2212,2042],{"stretchy":2036},[2034,2214,2215],{},">",[2217,2218,2219],"mn",{},"0",[1994,2221,2222],{"encoding":1996},"u'(W)>0",[1971,2224,2226,2298],{"className":2225,"ariaHidden":2001},[2000],[1971,2227,2229,2233,2277,2280,2283,2286,2291,2295],{"className":2228},[2005],[1971,2230],{"className":2231,"style":2232},[2009],"height:1.0019em;vertical-align:-0.25em;",[1971,2234,2236,2239],{"className":2235},[2014],[1971,2237,2032],{"className":2238},[2014,2015],[1971,2240,2243],{"className":2241},[2242],"msupsub",[1971,2244,2247],{"className":2245},[2246],"vlist-t",[1971,2248,2251],{"className":2249},[2250],"vlist-r",[1971,2252,2256],{"className":2253,"style":2255},[2254],"vlist","height:0.7519em;",[1971,2257,2259,2264],{"style":2258},"top:-3.063em;margin-right:0.05em;",[1971,2260],{"className":2261,"style":2263},[2262],"pstrut","height:2.7em;",[1971,2265,2271],{"className":2266},[2267,2268,2269,2270],"sizing","reset-size6","size3","mtight",[1971,2272,2274],{"className":2273},[2014,2270],[1971,2275,2206],{"className":2276},[2014,2270],[1971,2278,2037],{"className":2279},[2062],[1971,2281,1992],{"className":2282,"style":2016},[2014,2015],[1971,2284,2042],{"className":2285},[2069],[1971,2287],{"className":2288,"style":2290},[2289],"mspace","margin-right:0.2778em;",[1971,2292,2215],{"className":2293},[2294],"mrel",[1971,2296],{"className":2297,"style":2290},[2289],[1971,2299,2301,2305],{"className":2300},[2005],[1971,2302],{"className":2303,"style":2304},[2009],"height:0.6444em;",[1971,2306,2219],{"className":2307},[2014],"，更多财富更好；若 ",[1971,2310,2312,2345],{"className":2311},[1974],[1971,2313,2315],{"className":2314},[1978],[1980,2316,2317],{"xmlns":1982},[1984,2318,2319,2342],{},[1987,2320,2321,2331,2333,2335,2337,2340],{},[2198,2322,2323,2325],{},[1990,2324,2032],{},[1987,2326,2327,2329],{},[2034,2328,2206],{"mathvariant":2204},[2034,2330,2206],{"mathvariant":2204},[2034,2332,2037],{"stretchy":2036},[1990,2334,1992],{},[2034,2336,2042],{"stretchy":2036},[2034,2338,2339],{},"\u003C",[2217,2341,2219],{},[1994,2343,2344],{"encoding":1996},"u''(W)\u003C0",[1971,2346,2348,2405],{"className":2347,"ariaHidden":2001},[2000],[1971,2349,2351,2354,2387,2390,2393,2396,2399,2402],{"className":2350},[2005],[1971,2352],{"className":2353,"style":2232},[2009],[1971,2355,2357,2360],{"className":2356},[2014],[1971,2358,2032],{"className":2359},[2014,2015],[1971,2361,2363],{"className":2362},[2242],[1971,2364,2366],{"className":2365},[2246],[1971,2367,2369],{"className":2368},[2250],[1971,2370,2372],{"className":2371,"style":2255},[2254],[1971,2373,2374,2377],{"style":2258},[1971,2375],{"className":2376,"style":2263},[2262],[1971,2378,2380],{"className":2379},[2267,2268,2269,2270],[1971,2381,2383],{"className":2382},[2014,2270],[1971,2384,2386],{"className":2385},[2014,2270],"′′",[1971,2388,2037],{"className":2389},[2062],[1971,2391,1992],{"className":2392,"style":2016},[2014,2015],[1971,2394,2042],{"className":2395},[2069],[1971,2397],{"className":2398,"style":2290},[2289],[1971,2400,2339],{"className":2401},[2294],[1971,2403],{"className":2404,"style":2290},[2289],[1971,2406,2408,2411],{"className":2407},[2005],[1971,2409],{"className":2410,"style":2304},[2009],[1971,2412,2219],{"className":2413},[2014],"，边际效用递减，说明同样 1 元钱在低财富状态更有价值。",[1793,2416,2417],{},"这条直觉非常重要：风险资产如果在低财富、坏经济状态中支付少，它会降低最宝贵状态下的财富，因此必须提供更高的平均收益作为补偿。",[2419,2420],"mermaid-diagram",{"code64":2421,"locale":7},"Zmxvd2NoYXJ0IExSCiAgQVsi6ZqP5py66LSi5a+MIFciXSAtLT4gQlsi5pWI55So5Ye95pWwIHUoVykiXQogIEIgLS0+IENbIuacn+acm+aViOeUqCBFW3UoVyldIl0KICBDIC0tPiBEWyLnoa7lrprmgKfnrYnku7cgQ0UiXQogIEQgLS0+IEVbIumjjumZqea6ouS7tyBSUCJd",[1800,2423,2424],{"id":2424},"关键定义与定理",[2426,2427,2428],"h3",{"id":2428},"期望效用",[1793,2430,2431,2432,2731],{},"彩票 ",[1971,2433,2435,2498],{"className":2434},[1974],[1971,2436,2438],{"className":2437},[1978],[1980,2439,2440],{"xmlns":1982},[1984,2441,2442,2495],{},[1987,2443,2444,2447,2450,2452,2460,2463,2470,2473,2476,2478,2485,2487,2493],{},[1990,2445,2446],{},"L",[2034,2448,2449],{},"=",[2034,2451,2037],{"stretchy":2036},[2453,2454,2455,2457],"msub",{},[1990,2456,1793],{},[2217,2458,2459],{},"1",[2034,2461,2462],{"separator":2001},",",[2453,2464,2465,2468],{},[1990,2466,2467],{},"x",[2217,2469,2459],{},[2034,2471,2472],{"separator":2001},";",[2034,2474,2475],{},"…",[2034,2477,2472],{"separator":2001},[2453,2479,2480,2482],{},[1990,2481,1793],{},[1990,2483,2484],{},"n",[2034,2486,2462],{"separator":2001},[2453,2488,2489,2491],{},[1990,2490,2467],{},[1990,2492,2484],{},[2034,2494,2042],{"stretchy":2036},[1994,2496,2497],{"encoding":1996},"L=(p_1,x_1;\\ldots;p_n,x_n)",[1971,2499,2501,2519],{"className":2500,"ariaHidden":2001},[2000],[1971,2502,2504,2507,2510,2513,2516],{"className":2503},[2005],[1971,2505],{"className":2506,"style":2010},[2009],[1971,2508,2446],{"className":2509},[2014,2015],[1971,2511],{"className":2512,"style":2290},[2289],[1971,2514,2449],{"className":2515},[2294],[1971,2517],{"className":2518,"style":2290},[2289],[1971,2520,2522,2525,2528,2574,2578,2582,2622,2625,2628,2632,2635,2638,2641,2682,2685,2688,2728],{"className":2521},[2005],[1971,2523],{"className":2524,"style":2055},[2009],[1971,2526,2037],{"className":2527},[2062],[1971,2529,2531,2534],{"className":2530},[2014],[1971,2532,1793],{"className":2533},[2014,2015],[1971,2535,2537],{"className":2536},[2242],[1971,2538,2541,2565],{"className":2539},[2246,2540],"vlist-t2",[1971,2542,2544,2560],{"className":2543},[2250],[1971,2545,2548],{"className":2546,"style":2547},[2254],"height:0.3011em;",[1971,2549,2551,2554],{"style":2550},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1971,2552],{"className":2553,"style":2263},[2262],[1971,2555,2557],{"className":2556},[2267,2268,2269,2270],[1971,2558,2459],{"className":2559},[2014,2270],[1971,2561,2564],{"className":2562},[2563],"vlist-s","​",[1971,2566,2568],{"className":2567},[2250],[1971,2569,2572],{"className":2570,"style":2571},[2254],"height:0.15em;",[1971,2573],{},[1971,2575,2462],{"className":2576},[2577],"mpunct",[1971,2579],{"className":2580,"style":2581},[2289],"margin-right:0.1667em;",[1971,2583,2585,2588],{"className":2584},[2014],[1971,2586,2467],{"className":2587},[2014,2015],[1971,2589,2591],{"className":2590},[2242],[1971,2592,2594,2614],{"className":2593},[2246,2540],[1971,2595,2597,2611],{"className":2596},[2250],[1971,2598,2600],{"className":2599,"style":2547},[2254],[1971,2601,2602,2605],{"style":2550},[1971,2603],{"className":2604,"style":2263},[2262],[1971,2606,2608],{"className":2607},[2267,2268,2269,2270],[1971,2609,2459],{"className":2610},[2014,2270],[1971,2612,2564],{"className":2613},[2563],[1971,2615,2617],{"className":2616},[2250],[1971,2618,2620],{"className":2619,"style":2571},[2254],[1971,2621],{},[1971,2623,2472],{"className":2624},[2577],[1971,2626],{"className":2627,"style":2581},[2289],[1971,2629,2475],{"className":2630},[2631],"minner",[1971,2633],{"className":2634,"style":2581},[2289],[1971,2636,2472],{"className":2637},[2577],[1971,2639],{"className":2640,"style":2581},[2289],[1971,2642,2644,2647],{"className":2643},[2014],[1971,2645,1793],{"className":2646},[2014,2015],[1971,2648,2650],{"className":2649},[2242],[1971,2651,2653,2674],{"className":2652},[2246,2540],[1971,2654,2656,2671],{"className":2655},[2250],[1971,2657,2660],{"className":2658,"style":2659},[2254],"height:0.1514em;",[1971,2661,2662,2665],{"style":2550},[1971,2663],{"className":2664,"style":2263},[2262],[1971,2666,2668],{"className":2667},[2267,2268,2269,2270],[1971,2669,2484],{"className":2670},[2014,2015,2270],[1971,2672,2564],{"className":2673},[2563],[1971,2675,2677],{"className":2676},[2250],[1971,2678,2680],{"className":2679,"style":2571},[2254],[1971,2681],{},[1971,2683,2462],{"className":2684},[2577],[1971,2686],{"className":2687,"style":2581},[2289],[1971,2689,2691,2694],{"className":2690},[2014],[1971,2692,2467],{"className":2693},[2014,2015],[1971,2695,2697],{"className":2696},[2242],[1971,2698,2700,2720],{"className":2699},[2246,2540],[1971,2701,2703,2717],{"className":2702},[2250],[1971,2704,2706],{"className":2705,"style":2659},[2254],[1971,2707,2708,2711],{"style":2550},[1971,2709],{"className":2710,"style":2263},[2262],[1971,2712,2714],{"className":2713},[2267,2268,2269,2270],[1971,2715,2484],{"className":2716},[2014,2015,2270],[1971,2718,2564],{"className":2719},[2563],[1971,2721,2723],{"className":2722},[2250],[1971,2724,2726],{"className":2725,"style":2571},[2254],[1971,2727],{},[1971,2729,2042],{"className":2730},[2069]," 的期望效用为：",[1971,2733,2735],{"className":2734},[2074],[1971,2736,2738,2798],{"className":2737},[1974],[1971,2739,2741],{"className":2740},[1978],[1980,2742,2743],{"xmlns":1982,"display":2083},[1984,2744,2745,2795],{},[1987,2746,2747,2749,2752,2754,2756,2758,2760,2777,2783,2785,2787,2793],{},[1990,2748,2090],{},[1990,2750,2751],{},"U",[2034,2753,2037],{"stretchy":2036},[1990,2755,2446],{},[2034,2757,2042],{"stretchy":2036},[2034,2759,2449],{},[2761,2762,2763,2766,2775],"munderover",{},[2034,2764,2765],{},"∑",[1987,2767,2768,2771,2773],{},[1990,2769,2770],{},"i",[2034,2772,2449],{},[2217,2774,2459],{},[1990,2776,2484],{},[2453,2778,2779,2781],{},[1990,2780,1793],{},[1990,2782,2770],{},[1990,2784,2032],{},[2034,2786,2037],{"stretchy":2036},[2453,2788,2789,2791],{},[1990,2790,2467],{},[1990,2792,2770],{},[2034,2794,2042],{"stretchy":2036},[1994,2796,2797],{"encoding":1996},"EU(L)=\\sum_{i=1}^n p_i u(x_i)",[1971,2799,2801,2832],{"className":2800,"ariaHidden":2001},[2000],[1971,2802,2804,2807,2810,2814,2817,2820,2823,2826,2829],{"className":2803},[2005],[1971,2805],{"className":2806,"style":2055},[2009],[1971,2808,2090],{"className":2809,"style":2120},[2014,2015],[1971,2811,2751],{"className":2812,"style":2813},[2014,2015],"margin-right:0.109em;",[1971,2815,2037],{"className":2816},[2062],[1971,2818,2446],{"className":2819},[2014,2015],[1971,2821,2042],{"className":2822},[2069],[1971,2824],{"className":2825,"style":2290},[2289],[1971,2827,2449],{"className":2828},[2294],[1971,2830],{"className":2831,"style":2290},[2289],[1971,2833,2835,2839,2913,2916,2957,2960,2963,3003],{"className":2834},[2005],[1971,2836],{"className":2837,"style":2838},[2009],"height:2.9291em;vertical-align:-1.2777em;",[1971,2840,2844],{"className":2841},[2842,2843],"mop","op-limits",[1971,2845,2847,2904],{"className":2846},[2246,2540],[1971,2848,2850,2901],{"className":2849},[2250],[1971,2851,2854,2876,2889],{"className":2852,"style":2853},[2254],"height:1.6514em;",[1971,2855,2857,2861],{"style":2856},"top:-1.8723em;margin-left:0em;",[1971,2858],{"className":2859,"style":2860},[2262],"height:3.05em;",[1971,2862,2864],{"className":2863},[2267,2268,2269,2270],[1971,2865,2867,2870,2873],{"className":2866},[2014,2270],[1971,2868,2770],{"className":2869},[2014,2015,2270],[1971,2871,2449],{"className":2872},[2294,2270],[1971,2874,2459],{"className":2875},[2014,2270],[1971,2877,2879,2882],{"style":2878},"top:-3.05em;",[1971,2880],{"className":2881,"style":2860},[2262],[1971,2883,2884],{},[1971,2885,2765],{"className":2886},[2842,2887,2888],"op-symbol","large-op",[1971,2890,2892,2895],{"style":2891},"top:-4.3em;margin-left:0em;",[1971,2893],{"className":2894,"style":2860},[2262],[1971,2896,2898],{"className":2897},[2267,2268,2269,2270],[1971,2899,2484],{"className":2900},[2014,2015,2270],[1971,2902,2564],{"className":2903},[2563],[1971,2905,2907],{"className":2906},[2250],[1971,2908,2911],{"className":2909,"style":2910},[2254],"height:1.2777em;",[1971,2912],{},[1971,2914],{"className":2915,"style":2581},[2289],[1971,2917,2919,2922],{"className":2918},[2014],[1971,2920,1793],{"className":2921},[2014,2015],[1971,2923,2925],{"className":2924},[2242],[1971,2926,2928,2949],{"className":2927},[2246,2540],[1971,2929,2931,2946],{"className":2930},[2250],[1971,2932,2935],{"className":2933,"style":2934},[2254],"height:0.3117em;",[1971,2936,2937,2940],{"style":2550},[1971,2938],{"className":2939,"style":2263},[2262],[1971,2941,2943],{"className":2942},[2267,2268,2269,2270],[1971,2944,2770],{"className":2945},[2014,2015,2270],[1971,2947,2564],{"className":2948},[2563],[1971,2950,2952],{"className":2951},[2250],[1971,2953,2955],{"className":2954,"style":2571},[2254],[1971,2956],{},[1971,2958,2032],{"className":2959},[2014,2015],[1971,2961,2037],{"className":2962},[2062],[1971,2964,2966,2969],{"className":2965},[2014],[1971,2967,2467],{"className":2968},[2014,2015],[1971,2970,2972],{"className":2971},[2242],[1971,2973,2975,2995],{"className":2974},[2246,2540],[1971,2976,2978,2992],{"className":2977},[2250],[1971,2979,2981],{"className":2980,"style":2934},[2254],[1971,2982,2983,2986],{"style":2550},[1971,2984],{"className":2985,"style":2263},[2262],[1971,2987,2989],{"className":2988},[2267,2268,2269,2270],[1971,2990,2770],{"className":2991},[2014,2015,2270],[1971,2993,2564],{"className":2994},[2563],[1971,2996,2998],{"className":2997},[2250],[1971,2999,3001],{"className":3000,"style":2571},[2254],[1971,3002],{},[1971,3004,2042],{"className":3005},[2069],[1793,3007,3008],{},"中文解释：不是先把金额平均再取效用，而是先对每个结果取效用，再按概率平均。",[2426,3010,3011],{"id":3011},"风险厌恶",[1793,3013,3014],{},"若投资者对任意公平赌博都不愿意接受，则称其风险厌恶。充分常用的数学条件是：",[1971,3016,3018],{"className":3017},[2074],[1971,3019,3021,3052],{"className":3020},[1974],[1971,3022,3024],{"className":3023},[1978],[1980,3025,3026],{"xmlns":1982,"display":2083},[1984,3027,3028,3050],{},[1987,3029,3030,3040,3042,3044,3046,3048],{},[2198,3031,3032,3034],{},[1990,3033,2032],{},[1987,3035,3036,3038],{},[2034,3037,2206],{"mathvariant":2204},[2034,3039,2206],{"mathvariant":2204},[2034,3041,2037],{"stretchy":2036},[1990,3043,1992],{},[2034,3045,2042],{"stretchy":2036},[2034,3047,2339],{},[2217,3049,2219],{},[1994,3051,2344],{"encoding":1996},[1971,3053,3055,3114],{"className":3054,"ariaHidden":2001},[2000],[1971,3056,3058,3062,3096,3099,3102,3105,3108,3111],{"className":3057},[2005],[1971,3059],{"className":3060,"style":3061},[2009],"height:1.0519em;vertical-align:-0.25em;",[1971,3063,3065,3068],{"className":3064},[2014],[1971,3066,2032],{"className":3067},[2014,2015],[1971,3069,3071],{"className":3070},[2242],[1971,3072,3074],{"className":3073},[2246],[1971,3075,3077],{"className":3076},[2250],[1971,3078,3081],{"className":3079,"style":3080},[2254],"height:0.8019em;",[1971,3082,3084,3087],{"style":3083},"top:-3.113em;margin-right:0.05em;",[1971,3085],{"className":3086,"style":2263},[2262],[1971,3088,3090],{"className":3089},[2267,2268,2269,2270],[1971,3091,3093],{"className":3092},[2014,2270],[1971,3094,2386],{"className":3095},[2014,2270],[1971,3097,2037],{"className":3098},[2062],[1971,3100,1992],{"className":3101,"style":2016},[2014,2015],[1971,3103,2042],{"className":3104},[2069],[1971,3106],{"className":3107,"style":2290},[2289],[1971,3109,2339],{"className":3110},[2294],[1971,3112],{"className":3113,"style":2290},[2289],[1971,3115,3117,3120],{"className":3116},[2005],[1971,3118],{"className":3119,"style":2304},[2009],[1971,3121,2219],{"className":3122},[2014],[1793,3124,3125],{},"中文解释：效用函数凹，代表损失 1 元带来的痛苦大于获得 1 元带来的快乐。",[2426,3127,3129],{"id":3128},"arrow-pratt-风险厌恶系数","Arrow-Pratt 风险厌恶系数",[1793,3131,3132],{},"绝对风险厌恶：",[1971,3134,3136],{"className":3135},[2074],[1971,3137,3139,3200],{"className":3138},[1974],[1971,3140,3142],{"className":3141},[1978],[1980,3143,3144],{"xmlns":1982,"display":2083},[1984,3145,3146,3197],{},[1987,3147,3148,3151,3153,3155,3157,3159,3162],{},[1990,3149,3150],{},"A",[2034,3152,2037],{"stretchy":2036},[1990,3154,1992],{},[2034,3156,2042],{"stretchy":2036},[2034,3158,2449],{},[2034,3160,3161],{},"−",[3163,3164,3165,3183],"mfrac",{},[1987,3166,3167,3177,3179,3181],{},[2198,3168,3169,3171],{},[1990,3170,2032],{},[1987,3172,3173,3175],{},[2034,3174,2206],{"mathvariant":2204},[2034,3176,2206],{"mathvariant":2204},[2034,3178,2037],{"stretchy":2036},[1990,3180,1992],{},[2034,3182,2042],{"stretchy":2036},[1987,3184,3185,3191,3193,3195],{},[2198,3186,3187,3189],{},[1990,3188,2032],{},[2034,3190,2206],{"mathvariant":2204,"lspace":2205,"rspace":2205},[2034,3192,2037],{"stretchy":2036},[1990,3194,1992],{},[2034,3196,2042],{"stretchy":2036},[1994,3198,3199],{"encoding":1996},"A(W)=-\\frac{u''(W)}{u'(W)}",[1971,3201,3203,3230],{"className":3202,"ariaHidden":2001},[2000],[1971,3204,3206,3209,3212,3215,3218,3221,3224,3227],{"className":3205},[2005],[1971,3207],{"className":3208,"style":2055},[2009],[1971,3210,3150],{"className":3211},[2014,2015],[1971,3213,2037],{"className":3214},[2062],[1971,3216,1992],{"className":3217,"style":2016},[2014,2015],[1971,3219,2042],{"className":3220},[2069],[1971,3222],{"className":3223,"style":2290},[2289],[1971,3225,2449],{"className":3226},[2294],[1971,3228],{"className":3229,"style":2290},[2289],[1971,3231,3233,3237,3240],{"className":3232},[2005],[1971,3234],{"className":3235,"style":3236},[2009],"height:2.3649em;vertical-align:-0.936em;",[1971,3238,3161],{"className":3239},[2014],[1971,3241,3243,3247,3386],{"className":3242},[2014],[1971,3244],{"className":3245},[2062,3246],"nulldelimiter",[1971,3248,3250],{"className":3249},[3163],[1971,3251,3253,3377],{"className":3252},[2246,2540],[1971,3254,3256,3374],{"className":3255},[2250],[1971,3257,3260,3313,3324],{"className":3258,"style":3259},[2254],"height:1.4289em;",[1971,3261,3263,3267],{"style":3262},"top:-2.314em;",[1971,3264],{"className":3265,"style":3266},[2262],"height:3em;",[1971,3268,3270,3304,3307,3310],{"className":3269},[2014],[1971,3271,3273,3276],{"className":3272},[2014],[1971,3274,2032],{"className":3275},[2014,2015],[1971,3277,3279],{"className":3278},[2242],[1971,3280,3282],{"className":3281},[2246],[1971,3283,3285],{"className":3284},[2250],[1971,3286,3289],{"className":3287,"style":3288},[2254],"height:0.6779em;",[1971,3290,3292,3295],{"style":3291},"top:-2.989em;margin-right:0.05em;",[1971,3293],{"className":3294,"style":2263},[2262],[1971,3296,3298],{"className":3297},[2267,2268,2269,2270],[1971,3299,3301],{"className":3300},[2014,2270],[1971,3302,2206],{"className":3303},[2014,2270],[1971,3305,2037],{"className":3306},[2062],[1971,3308,1992],{"className":3309,"style":2016},[2014,2015],[1971,3311,2042],{"className":3312},[2069],[1971,3314,3316,3319],{"style":3315},"top:-3.23em;",[1971,3317],{"className":3318,"style":3266},[2262],[1971,3320],{"className":3321,"style":3323},[3322],"frac-line","border-bottom-width:0.04em;",[1971,3325,3327,3330],{"style":3326},"top:-3.677em;",[1971,3328],{"className":3329,"style":3266},[2262],[1971,3331,3333,3365,3368,3371],{"className":3332},[2014],[1971,3334,3336,3339],{"className":3335},[2014],[1971,3337,2032],{"className":3338},[2014,2015],[1971,3340,3342],{"className":3341},[2242],[1971,3343,3345],{"className":3344},[2246],[1971,3346,3348],{"className":3347},[2250],[1971,3349,3351],{"className":3350,"style":2255},[2254],[1971,3352,3353,3356],{"style":2258},[1971,3354],{"className":3355,"style":2263},[2262],[1971,3357,3359],{"className":3358},[2267,2268,2269,2270],[1971,3360,3362],{"className":3361},[2014,2270],[1971,3363,2386],{"className":3364},[2014,2270],[1971,3366,2037],{"className":3367},[2062],[1971,3369,1992],{"className":3370,"style":2016},[2014,2015],[1971,3372,2042],{"className":3373},[2069],[1971,3375,2564],{"className":3376},[2563],[1971,3378,3380],{"className":3379},[2250],[1971,3381,3384],{"className":3382,"style":3383},[2254],"height:0.936em;",[1971,3385],{},[1971,3387],{"className":3388},[2069,3246],[1793,3390,3391],{},"相对风险厌恶：",[1971,3393,3395],{"className":3394},[2074],[1971,3396,3398,3459],{"className":3397},[1974],[1971,3399,3401],{"className":3400},[1978],[1980,3402,3403],{"xmlns":1982,"display":2083},[1984,3404,3405,3456],{},[1987,3406,3407,3410,3412,3414,3416,3418,3420,3422],{},[1990,3408,3409],{},"R",[2034,3411,2037],{"stretchy":2036},[1990,3413,1992],{},[2034,3415,2042],{"stretchy":2036},[2034,3417,2449],{},[2034,3419,3161],{},[1990,3421,1992],{},[3163,3423,3424,3442],{},[1987,3425,3426,3436,3438,3440],{},[2198,3427,3428,3430],{},[1990,3429,2032],{},[1987,3431,3432,3434],{},[2034,3433,2206],{"mathvariant":2204},[2034,3435,2206],{"mathvariant":2204},[2034,3437,2037],{"stretchy":2036},[1990,3439,1992],{},[2034,3441,2042],{"stretchy":2036},[1987,3443,3444,3450,3452,3454],{},[2198,3445,3446,3448],{},[1990,3447,2032],{},[2034,3449,2206],{"mathvariant":2204,"lspace":2205,"rspace":2205},[2034,3451,2037],{"stretchy":2036},[1990,3453,1992],{},[2034,3455,2042],{"stretchy":2036},[1994,3457,3458],{"encoding":1996},"R(W)=-W\\frac{u''(W)}{u'(W)}",[1971,3460,3462,3490],{"className":3461,"ariaHidden":2001},[2000],[1971,3463,3465,3468,3472,3475,3478,3481,3484,3487],{"className":3464},[2005],[1971,3466],{"className":3467,"style":2055},[2009],[1971,3469,3409],{"className":3470,"style":3471},[2014,2015],"margin-right:0.0077em;",[1971,3473,2037],{"className":3474},[2062],[1971,3476,1992],{"className":3477,"style":2016},[2014,2015],[1971,3479,2042],{"className":3480},[2069],[1971,3482],{"className":3483,"style":2290},[2289],[1971,3485,2449],{"className":3486},[2294],[1971,3488],{"className":3489,"style":2290},[2289],[1971,3491,3493,3496,3499,3502],{"className":3492},[2005],[1971,3494],{"className":3495,"style":3236},[2009],[1971,3497,3161],{"className":3498},[2014],[1971,3500,1992],{"className":3501,"style":2016},[2014,2015],[1971,3503,3505,3508,3637],{"className":3504},[2014],[1971,3506],{"className":3507},[2062,3246],[1971,3509,3511],{"className":3510},[3163],[1971,3512,3514,3629],{"className":3513},[2246,2540],[1971,3515,3517,3626],{"className":3516},[2250],[1971,3518,3520,3569,3577],{"className":3519,"style":3259},[2254],[1971,3521,3522,3525],{"style":3262},[1971,3523],{"className":3524,"style":3266},[2262],[1971,3526,3528,3560,3563,3566],{"className":3527},[2014],[1971,3529,3531,3534],{"className":3530},[2014],[1971,3532,2032],{"className":3533},[2014,2015],[1971,3535,3537],{"className":3536},[2242],[1971,3538,3540],{"className":3539},[2246],[1971,3541,3543],{"className":3542},[2250],[1971,3544,3546],{"className":3545,"style":3288},[2254],[1971,3547,3548,3551],{"style":3291},[1971,3549],{"className":3550,"style":2263},[2262],[1971,3552,3554],{"className":3553},[2267,2268,2269,2270],[1971,3555,3557],{"className":3556},[2014,2270],[1971,3558,2206],{"className":3559},[2014,2270],[1971,3561,2037],{"className":3562},[2062],[1971,3564,1992],{"className":3565,"style":2016},[2014,2015],[1971,3567,2042],{"className":3568},[2069],[1971,3570,3571,3574],{"style":3315},[1971,3572],{"className":3573,"style":3266},[2262],[1971,3575],{"className":3576,"style":3323},[3322],[1971,3578,3579,3582],{"style":3326},[1971,3580],{"className":3581,"style":3266},[2262],[1971,3583,3585,3617,3620,3623],{"className":3584},[2014],[1971,3586,3588,3591],{"className":3587},[2014],[1971,3589,2032],{"className":3590},[2014,2015],[1971,3592,3594],{"className":3593},[2242],[1971,3595,3597],{"className":3596},[2246],[1971,3598,3600],{"className":3599},[2250],[1971,3601,3603],{"className":3602,"style":2255},[2254],[1971,3604,3605,3608],{"style":2258},[1971,3606],{"className":3607,"style":2263},[2262],[1971,3609,3611],{"className":3610},[2267,2268,2269,2270],[1971,3612,3614],{"className":3613},[2014,2270],[1971,3615,2386],{"className":3616},[2014,2270],[1971,3618,2037],{"className":3619},[2062],[1971,3621,1992],{"className":3622,"style":2016},[2014,2015],[1971,3624,2042],{"className":3625},[2069],[1971,3627,2564],{"className":3628},[2563],[1971,3630,3632],{"className":3631},[2250],[1971,3633,3635],{"className":3634,"style":3383},[2254],[1971,3636],{},[1971,3638],{"className":3639},[2069,3246],[1793,3641,3642,3643,3687,3688,3732],{},"中文解释：",[1971,3644,3646,3666],{"className":3645},[1974],[1971,3647,3649],{"className":3648},[1978],[1980,3650,3651],{"xmlns":1982},[1984,3652,3653,3663],{},[1987,3654,3655,3657,3659,3661],{},[1990,3656,3150],{},[2034,3658,2037],{"stretchy":2036},[1990,3660,1992],{},[2034,3662,2042],{"stretchy":2036},[1994,3664,3665],{"encoding":1996},"A(W)",[1971,3667,3669],{"className":3668,"ariaHidden":2001},[2000],[1971,3670,3672,3675,3678,3681,3684],{"className":3671},[2005],[1971,3673],{"className":3674,"style":2055},[2009],[1971,3676,3150],{"className":3677},[2014,2015],[1971,3679,2037],{"className":3680},[2062],[1971,3682,1992],{"className":3683,"style":2016},[2014,2015],[1971,3685,2042],{"className":3686},[2069]," 更适合讨论固定金额风险，例如是否买保险；",[1971,3689,3691,3711],{"className":3690},[1974],[1971,3692,3694],{"className":3693},[1978],[1980,3695,3696],{"xmlns":1982},[1984,3697,3698,3708],{},[1987,3699,3700,3702,3704,3706],{},[1990,3701,3409],{},[2034,3703,2037],{"stretchy":2036},[1990,3705,1992],{},[2034,3707,2042],{"stretchy":2036},[1994,3709,3710],{"encoding":1996},"R(W)",[1971,3712,3714],{"className":3713,"ariaHidden":2001},[2000],[1971,3715,3717,3720,3723,3726,3729],{"className":3716},[2005],[1971,3718],{"className":3719,"style":2055},[2009],[1971,3721,3409],{"className":3722,"style":3471},[2014,2015],[1971,3724,2037],{"className":3725},[2062],[1971,3727,1992],{"className":3728,"style":2016},[2014,2015],[1971,3730,2042],{"className":3731},[2069]," 更适合讨论按财富比例投资风险资产，例如股票配置比例。",[2426,3734,3735],{"id":3735},"确定性等价与风险溢价",[1793,3737,3738,3739,3775],{},"确定性等价 ",[1971,3740,3742,3759],{"className":3741},[1974],[1971,3743,3745],{"className":3744},[1978],[1980,3746,3747],{"xmlns":1982},[1984,3748,3749,3756],{},[1987,3750,3751,3754],{},[1990,3752,3753],{},"C",[1990,3755,2090],{},[1994,3757,3758],{"encoding":1996},"CE",[1971,3760,3762],{"className":3761,"ariaHidden":2001},[2000],[1971,3763,3765,3768,3772],{"className":3764},[2005],[1971,3766],{"className":3767,"style":2010},[2009],[1971,3769,3753],{"className":3770,"style":3771},[2014,2015],"margin-right:0.0715em;",[1971,3773,2090],{"className":3774,"style":2120},[2014,2015]," 满足：",[1971,3777,3779],{"className":3778},[2074],[1971,3780,3782,3820],{"className":3781},[1974],[1971,3783,3785],{"className":3784},[1978],[1980,3786,3787],{"xmlns":1982,"display":2083},[1984,3788,3789,3817],{},[1987,3790,3791,3793,3795,3797,3799,3801,3803,3805,3807,3809,3811,3813,3815],{},[1990,3792,2032],{},[2034,3794,2037],{"stretchy":2036},[1990,3796,3753],{},[1990,3798,2090],{},[2034,3800,2042],{"stretchy":2036},[2034,3802,2449],{},[1990,3804,2090],{},[2034,3806,2093],{"stretchy":2036},[1990,3808,2032],{},[2034,3810,2037],{"stretchy":2036},[1990,3812,1992],{},[2034,3814,2042],{"stretchy":2036},[2034,3816,2104],{"stretchy":2036},[1994,3818,3819],{"encoding":1996},"u(CE)=E[u(W)]",[1971,3821,3823,3853],{"className":3822,"ariaHidden":2001},[2000],[1971,3824,3826,3829,3832,3835,3838,3841,3844,3847,3850],{"className":3825},[2005],[1971,3827],{"className":3828,"style":2055},[2009],[1971,3830,2032],{"className":3831},[2014,2015],[1971,3833,2037],{"className":3834},[2062],[1971,3836,3753],{"className":3837,"style":3771},[2014,2015],[1971,3839,2090],{"className":3840,"style":2120},[2014,2015],[1971,3842,2042],{"className":3843},[2069],[1971,3845],{"className":3846,"style":2290},[2289],[1971,3848,2449],{"className":3849},[2294],[1971,3851],{"className":3852,"style":2290},[2289],[1971,3854,3856,3859,3862,3865,3868,3871,3874],{"className":3855},[2005],[1971,3857],{"className":3858,"style":2055},[2009],[1971,3860,2090],{"className":3861,"style":2120},[2014,2015],[1971,3863,2093],{"className":3864},[2062],[1971,3866,2032],{"className":3867},[2014,2015],[1971,3869,2037],{"className":3870},[2062],[1971,3872,1992],{"className":3873,"style":2016},[2014,2015],[1971,3875,2136],{"className":3876},[2069],[1793,3878,3879],{},"风险溢价为：",[1971,3881,3883],{"className":3882},[2074],[1971,3884,3886,3919],{"className":3885},[1974],[1971,3887,3889],{"className":3888},[1978],[1980,3890,3891],{"xmlns":1982,"display":2083},[1984,3892,3893,3916],{},[1987,3894,3895,3897,3900,3902,3904,3906,3908,3910,3912,3914],{},[1990,3896,3409],{},[1990,3898,3899],{},"P",[2034,3901,2449],{},[1990,3903,2090],{},[2034,3905,2093],{"stretchy":2036},[1990,3907,1992],{},[2034,3909,2104],{"stretchy":2036},[2034,3911,3161],{},[1990,3913,3753],{},[1990,3915,2090],{},[1994,3917,3918],{"encoding":1996},"RP=E[W]-CE",[1971,3920,3922,3943,3972],{"className":3921,"ariaHidden":2001},[2000],[1971,3923,3925,3928,3931,3934,3937,3940],{"className":3924},[2005],[1971,3926],{"className":3927,"style":2010},[2009],[1971,3929,3409],{"className":3930,"style":3471},[2014,2015],[1971,3932,3899],{"className":3933,"style":2016},[2014,2015],[1971,3935],{"className":3936,"style":2290},[2289],[1971,3938,2449],{"className":3939},[2294],[1971,3941],{"className":3942,"style":2290},[2289],[1971,3944,3946,3949,3952,3955,3958,3961,3965,3969],{"className":3945},[2005],[1971,3947],{"className":3948,"style":2055},[2009],[1971,3950,2090],{"className":3951,"style":2120},[2014,2015],[1971,3953,2093],{"className":3954},[2062],[1971,3956,1992],{"className":3957,"style":2016},[2014,2015],[1971,3959,2104],{"className":3960},[2069],[1971,3962],{"className":3963,"style":3964},[2289],"margin-right:0.2222em;",[1971,3966,3161],{"className":3967},[3968],"mbin",[1971,3970],{"className":3971,"style":3964},[2289],[1971,3973,3975,3978,3981],{"className":3974},[2005],[1971,3976],{"className":3977,"style":2010},[2009],[1971,3979,3753],{"className":3980,"style":3771},[2014,2015],[1971,3982,2090],{"className":3983,"style":2120},[2014,2015],[1793,3985,3642,3986,4019,4020,4054],{},[1971,3987,3989,4004],{"className":3988},[1974],[1971,3990,3992],{"className":3991},[1978],[1980,3993,3994],{"xmlns":1982},[1984,3995,3996,4002],{},[1987,3997,3998,4000],{},[1990,3999,3753],{},[1990,4001,2090],{},[1994,4003,3758],{"encoding":1996},[1971,4005,4007],{"className":4006,"ariaHidden":2001},[2000],[1971,4008,4010,4013,4016],{"className":4009},[2005],[1971,4011],{"className":4012,"style":2010},[2009],[1971,4014,3753],{"className":4015,"style":3771},[2014,2015],[1971,4017,2090],{"className":4018,"style":2120},[2014,2015]," 是投资者认为“和这个风险彩票一样好”的确定金额；",[1971,4021,4023,4039],{"className":4022},[1974],[1971,4024,4026],{"className":4025},[1978],[1980,4027,4028],{"xmlns":1982},[1984,4029,4030,4036],{},[1987,4031,4032,4034],{},[1990,4033,3409],{},[1990,4035,3899],{},[1994,4037,4038],{"encoding":1996},"RP",[1971,4040,4042],{"className":4041,"ariaHidden":2001},[2000],[1971,4043,4045,4048,4051],{"className":4044},[2005],[1971,4046],{"className":4047,"style":2010},[2009],[1971,4049,3409],{"className":4050,"style":3471},[2014,2015],[1971,4052,3899],{"className":4053,"style":2016},[2014,2015]," 是投资者愿意放弃的平均收益，以避免风险。",[1800,4056,4058],{"id":4057},"例子从期望收益到确定性等价","例子：从期望收益到确定性等价",[1793,4060,4061,4062,4193],{},"某投资者效用函数为 ",[1971,4063,4065,4092],{"className":4064},[1974],[1971,4066,4068],{"className":4067},[1978],[1980,4069,4070],{"xmlns":1982},[1984,4071,4072,4089],{},[1987,4073,4074,4076,4078,4080,4082,4084],{},[1990,4075,2032],{},[2034,4077,2037],{"stretchy":2036},[1990,4079,1992],{},[2034,4081,2042],{"stretchy":2036},[2034,4083,2449],{},[4085,4086,4087],"msqrt",{},[1990,4088,1992],{},[1994,4090,4091],{"encoding":1996},"u(W)=\\sqrt{W}",[1971,4093,4095,4122],{"className":4094,"ariaHidden":2001},[2000],[1971,4096,4098,4101,4104,4107,4110,4113,4116,4119],{"className":4097},[2005],[1971,4099],{"className":4100,"style":2055},[2009],[1971,4102,2032],{"className":4103},[2014,2015],[1971,4105,2037],{"className":4106},[2062],[1971,4108,1992],{"className":4109,"style":2016},[2014,2015],[1971,4111,2042],{"className":4112},[2069],[1971,4114],{"className":4115,"style":2290},[2289],[1971,4117,2449],{"className":4118},[2294],[1971,4120],{"className":4121,"style":2290},[2289],[1971,4123,4125,4129],{"className":4124},[2005],[1971,4126],{"className":4127,"style":4128},[2009],"height:1.04em;vertical-align:-0.1133em;",[1971,4130,4133],{"className":4131},[2014,4132],"sqrt",[1971,4134,4136,4184],{"className":4135},[2246,2540],[1971,4137,4139,4181],{"className":4138},[2250],[1971,4140,4143,4158],{"className":4141,"style":4142},[2254],"height:0.9267em;",[1971,4144,4148,4151],{"className":4145,"style":4147},[4146],"svg-align","top:-3em;",[1971,4149],{"className":4150,"style":3266},[2262],[1971,4152,4155],{"className":4153,"style":4154},[2014],"padding-left:0.833em;",[1971,4156,1992],{"className":4157,"style":2016},[2014,2015],[1971,4159,4161,4164],{"style":4160},"top:-2.8867em;",[1971,4162],{"className":4163,"style":3266},[2262],[1971,4165,4169],{"className":4166,"style":4168},[4167],"hide-tail","min-width:0.853em;height:1.08em;",[4170,4171,4177],"svg",{"xmlns":4172,"width":4173,"height":4174,"viewBox":4175,"preserveAspectRatio":4176},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[4178,4179],"path",{"d":4180},"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",[1971,4182,2564],{"className":4183},[2563],[1971,4185,4187],{"className":4186},[2250],[1971,4188,4191],{"className":4189,"style":4190},[2254],"height:0.1133em;",[1971,4192],{},"。有一种彩票：50% 概率得到 64，50% 概率得到 144。",[1793,4195,4196],{},"期望财富：",[1971,4198,4200],{"className":4199},[2074],[1971,4201,4203,4249],{"className":4202},[1974],[1971,4204,4206],{"className":4205},[1978],[1980,4207,4208],{"xmlns":1982,"display":2083},[1984,4209,4210,4246],{},[1987,4211,4212,4214,4216,4218,4220,4222,4225,4228,4231,4234,4236,4238,4241,4243],{},[1990,4213,2090],{},[2034,4215,2093],{"stretchy":2036},[1990,4217,1992],{},[2034,4219,2104],{"stretchy":2036},[2034,4221,2449],{},[2217,4223,4224],{},"0.5",[2034,4226,4227],{},"×",[2217,4229,4230],{},"64",[2034,4232,4233],{},"+",[2217,4235,4224],{},[2034,4237,4227],{},[2217,4239,4240],{},"144",[2034,4242,2449],{},[2217,4244,4245],{},"104",[1994,4247,4248],{"encoding":1996},"E[W]=0.5\\times64+0.5\\times144=104",[1971,4250,4252,4279,4298,4316,4334,4352],{"className":4251,"ariaHidden":2001},[2000],[1971,4253,4255,4258,4261,4264,4267,4270,4273,4276],{"className":4254},[2005],[1971,4256],{"className":4257,"style":2055},[2009],[1971,4259,2090],{"className":4260,"style":2120},[2014,2015],[1971,4262,2093],{"className":4263},[2062],[1971,4265,1992],{"className":4266,"style":2016},[2014,2015],[1971,4268,2104],{"className":4269},[2069],[1971,4271],{"className":4272,"style":2290},[2289],[1971,4274,2449],{"className":4275},[2294],[1971,4277],{"className":4278,"style":2290},[2289],[1971,4280,4282,4286,4289,4292,4295],{"className":4281},[2005],[1971,4283],{"className":4284,"style":4285},[2009],"height:0.7278em;vertical-align:-0.0833em;",[1971,4287,4224],{"className":4288},[2014],[1971,4290],{"className":4291,"style":3964},[2289],[1971,4293,4227],{"className":4294},[3968],[1971,4296],{"className":4297,"style":3964},[2289],[1971,4299,4301,4304,4307,4310,4313],{"className":4300},[2005],[1971,4302],{"className":4303,"style":4285},[2009],[1971,4305,4230],{"className":4306},[2014],[1971,4308],{"className":4309,"style":3964},[2289],[1971,4311,4233],{"className":4312},[3968],[1971,4314],{"className":4315,"style":3964},[2289],[1971,4317,4319,4322,4325,4328,4331],{"className":4318},[2005],[1971,4320],{"className":4321,"style":4285},[2009],[1971,4323,4224],{"className":4324},[2014],[1971,4326],{"className":4327,"style":3964},[2289],[1971,4329,4227],{"className":4330},[3968],[1971,4332],{"className":4333,"style":3964},[2289],[1971,4335,4337,4340,4343,4346,4349],{"className":4336},[2005],[1971,4338],{"className":4339,"style":2304},[2009],[1971,4341,4240],{"className":4342},[2014],[1971,4344],{"className":4345,"style":2290},[2289],[1971,4347,2449],{"className":4348},[2294],[1971,4350],{"className":4351,"style":2290},[2289],[1971,4353,4355,4358],{"className":4354},[2005],[1971,4356],{"className":4357,"style":2304},[2009],[1971,4359,4245],{"className":4360},[2014],[1793,4362,4363],{},"期望效用：",[1971,4365,4367],{"className":4366},[2074],[1971,4368,4370,4419],{"className":4369},[1974],[1971,4371,4373],{"className":4372},[1978],[1980,4374,4375],{"xmlns":1982,"display":2083},[1984,4376,4377,4416],{},[1987,4378,4379,4381,4383,4385,4387,4389,4391,4393,4395,4397,4399,4402,4404,4406,4408,4411,4413],{},[1990,4380,2090],{},[2034,4382,2093],{"stretchy":2036},[1990,4384,2032],{},[2034,4386,2037],{"stretchy":2036},[1990,4388,1992],{},[2034,4390,2042],{"stretchy":2036},[2034,4392,2104],{"stretchy":2036},[2034,4394,2449],{},[2217,4396,4224],{},[2034,4398,4227],{},[2217,4400,4401],{},"8",[2034,4403,4233],{},[2217,4405,4224],{},[2034,4407,4227],{},[2217,4409,4410],{},"12",[2034,4412,2449],{},[2217,4414,4415],{},"10",[1994,4417,4418],{"encoding":1996},"E[u(W)]=0.5\\times8+0.5\\times12=10",[1971,4420,4422,4455,4473,4491,4509,4527],{"className":4421,"ariaHidden":2001},[2000],[1971,4423,4425,4428,4431,4434,4437,4440,4443,4446,4449,4452],{"className":4424},[2005],[1971,4426],{"className":4427,"style":2055},[2009],[1971,4429,2090],{"className":4430,"style":2120},[2014,2015],[1971,4432,2093],{"className":4433},[2062],[1971,4435,2032],{"className":4436},[2014,2015],[1971,4438,2037],{"className":4439},[2062],[1971,4441,1992],{"className":4442,"style":2016},[2014,2015],[1971,4444,2136],{"className":4445},[2069],[1971,4447],{"className":4448,"style":2290},[2289],[1971,4450,2449],{"className":4451},[2294],[1971,4453],{"className":4454,"style":2290},[2289],[1971,4456,4458,4461,4464,4467,4470],{"className":4457},[2005],[1971,4459],{"className":4460,"style":4285},[2009],[1971,4462,4224],{"className":4463},[2014],[1971,4465],{"className":4466,"style":3964},[2289],[1971,4468,4227],{"className":4469},[3968],[1971,4471],{"className":4472,"style":3964},[2289],[1971,4474,4476,4479,4482,4485,4488],{"className":4475},[2005],[1971,4477],{"className":4478,"style":4285},[2009],[1971,4480,4401],{"className":4481},[2014],[1971,4483],{"className":4484,"style":3964},[2289],[1971,4486,4233],{"className":4487},[3968],[1971,4489],{"className":4490,"style":3964},[2289],[1971,4492,4494,4497,4500,4503,4506],{"className":4493},[2005],[1971,4495],{"className":4496,"style":4285},[2009],[1971,4498,4224],{"className":4499},[2014],[1971,4501],{"className":4502,"style":3964},[2289],[1971,4504,4227],{"className":4505},[3968],[1971,4507],{"className":4508,"style":3964},[2289],[1971,4510,4512,4515,4518,4521,4524],{"className":4511},[2005],[1971,4513],{"className":4514,"style":2304},[2009],[1971,4516,4410],{"className":4517},[2014],[1971,4519],{"className":4520,"style":2290},[2289],[1971,4522,2449],{"className":4523},[2294],[1971,4525],{"className":4526,"style":2290},[2289],[1971,4528,4530,4533],{"className":4529},[2005],[1971,4531],{"className":4532,"style":2304},[2009],[1971,4534,4415],{"className":4535},[2014],[1793,4537,4538,4539,4643],{},"确定性等价满足 ",[1971,4540,4542,4566],{"className":4541},[1974],[1971,4543,4545],{"className":4544},[1978],[1980,4546,4547],{"xmlns":1982},[1984,4548,4549,4563],{},[1987,4550,4551,4559,4561],{},[4085,4552,4553],{},[1987,4554,4555,4557],{},[1990,4556,3753],{},[1990,4558,2090],{},[2034,4560,2449],{},[2217,4562,4415],{},[1994,4564,4565],{"encoding":1996},"\\sqrt{CE}=10",[1971,4567,4569,4634],{"className":4568,"ariaHidden":2001},[2000],[1971,4570,4572,4575,4625,4628,4631],{"className":4571},[2005],[1971,4573],{"className":4574,"style":4128},[2009],[1971,4576,4578],{"className":4577},[2014,4132],[1971,4579,4581,4617],{"className":4580},[2246,2540],[1971,4582,4584,4614],{"className":4583},[2250],[1971,4585,4587,4602],{"className":4586,"style":4142},[2254],[1971,4588,4590,4593],{"className":4589,"style":4147},[4146],[1971,4591],{"className":4592,"style":3266},[2262],[1971,4594,4596,4599],{"className":4595,"style":4154},[2014],[1971,4597,3753],{"className":4598,"style":3771},[2014,2015],[1971,4600,2090],{"className":4601,"style":2120},[2014,2015],[1971,4603,4604,4607],{"style":4160},[1971,4605],{"className":4606,"style":3266},[2262],[1971,4608,4610],{"className":4609,"style":4168},[4167],[4170,4611,4612],{"xmlns":4172,"width":4173,"height":4174,"viewBox":4175,"preserveAspectRatio":4176},[4178,4613],{"d":4180},[1971,4615,2564],{"className":4616},[2563],[1971,4618,4620],{"className":4619},[2250],[1971,4621,4623],{"className":4622,"style":4190},[2254],[1971,4624],{},[1971,4626],{"className":4627,"style":2290},[2289],[1971,4629,2449],{"className":4630},[2294],[1971,4632],{"className":4633,"style":2290},[2289],[1971,4635,4637,4640],{"className":4636},[2005],[1971,4638],{"className":4639,"style":2304},[2009],[1971,4641,4415],{"className":4642},[2014],"，所以：",[1971,4645,4647],{"className":4646},[2074],[1971,4648,4650,4671],{"className":4649},[1974],[1971,4651,4653],{"className":4652},[1978],[1980,4654,4655],{"xmlns":1982,"display":2083},[1984,4656,4657,4668],{},[1987,4658,4659,4661,4663,4665],{},[1990,4660,3753],{},[1990,4662,2090],{},[2034,4664,2449],{},[2217,4666,4667],{},"100",[1994,4669,4670],{"encoding":1996},"CE=100",[1971,4672,4674,4695],{"className":4673,"ariaHidden":2001},[2000],[1971,4675,4677,4680,4683,4686,4689,4692],{"className":4676},[2005],[1971,4678],{"className":4679,"style":2010},[2009],[1971,4681,3753],{"className":4682,"style":3771},[2014,2015],[1971,4684,2090],{"className":4685,"style":2120},[2014,2015],[1971,4687],{"className":4688,"style":2290},[2289],[1971,4690,2449],{"className":4691},[2294],[1971,4693],{"className":4694,"style":2290},[2289],[1971,4696,4698,4701],{"className":4697},[2005],[1971,4699],{"className":4700,"style":2304},[2009],[1971,4702,4667],{"className":4703},[2014],[1793,4705,4706],{},"风险溢价：",[1971,4708,4710],{"className":4709},[2074],[1971,4711,4713,4742],{"className":4712},[1974],[1971,4714,4716],{"className":4715},[1978],[1980,4717,4718],{"xmlns":1982,"display":2083},[1984,4719,4720,4739],{},[1987,4721,4722,4724,4726,4728,4730,4732,4734,4736],{},[1990,4723,3409],{},[1990,4725,3899],{},[2034,4727,2449],{},[2217,4729,4245],{},[2034,4731,3161],{},[2217,4733,4667],{},[2034,4735,2449],{},[2217,4737,4738],{},"4",[1994,4740,4741],{"encoding":1996},"RP=104-100=4",[1971,4743,4745,4766,4784,4802],{"className":4744,"ariaHidden":2001},[2000],[1971,4746,4748,4751,4754,4757,4760,4763],{"className":4747},[2005],[1971,4749],{"className":4750,"style":2010},[2009],[1971,4752,3409],{"className":4753,"style":3471},[2014,2015],[1971,4755,3899],{"className":4756,"style":2016},[2014,2015],[1971,4758],{"className":4759,"style":2290},[2289],[1971,4761,2449],{"className":4762},[2294],[1971,4764],{"className":4765,"style":2290},[2289],[1971,4767,4769,4772,4775,4778,4781],{"className":4768},[2005],[1971,4770],{"className":4771,"style":4285},[2009],[1971,4773,4245],{"className":4774},[2014],[1971,4776],{"className":4777,"style":3964},[2289],[1971,4779,3161],{"className":4780},[3968],[1971,4782],{"className":4783,"style":3964},[2289],[1971,4785,4787,4790,4793,4796,4799],{"className":4786},[2005],[1971,4788],{"className":4789,"style":2304},[2009],[1971,4791,4667],{"className":4792},[2014],[1971,4794],{"className":4795,"style":2290},[2289],[1971,4797,2449],{"className":4798},[2294],[1971,4800],{"className":4801,"style":2290},[2289],[1971,4803,4805,4808],{"className":4804},[2005],[1971,4806],{"className":4807,"style":2304},[2009],[1971,4809,4738],{"className":4810},[2014],[1793,4812,4813],{},"这个结果说明，投资者并不是觉得彩票“值 104”，而是愿意用确定的 100 换掉它。4 就是承担该风险所需要的补偿。",[1800,4815,4817],{"id":4816},"可运行例题均值相同风险溢价可以不同","可运行例题：均值相同，风险溢价可以不同",[1793,4819,4820],{},"两种彩票的期望财富都为 104。第二种彩票把结果进一步拉开，是第一种彩票的均值保持扩散。",[4822,4823],"pyodide",{"code64":4824,"layout":4825,"locale":7,"title":4826},"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","vertical","Python：确定性等价与均值保持扩散",[1793,4828,4829],{},"凹效用下，更宽的彩票有更低确定性等价和更高风险溢价。这个方向来自风险厌恶；具体金额依赖效用函数和财富水平，不能当作所有投资者的统一市场价格。",[1800,4831,4832],{"id":4832},"学习顺序建议",[1804,4834,4835,4848],{},[1807,4836,4837],{},[1810,4838,4839,4842,4845],{},[1813,4840,4841],{},"小节",[1813,4843,4844],{},"先抓住的问题",[1813,4846,4847],{},"需要特别留意",[1820,4849,4850,4861,4872,4883,4893],{},[1810,4851,4852,4855,4858],{},[1825,4853,4854],{},"2.1 期望效用理论",[1825,4856,4857],{},"为什么比较的是期望效用而非期望金额",[1825,4859,4860],{},"独立性公理、正仿射变换",[1810,4862,4863,4866,4869],{},[1825,4864,4865],{},"2.2 风险厌恶与风险溢价",[1825,4867,4868],{},"凹效用如何生成风险溢价",[1825,4870,4871],{},"Jensen 不等式、Arrow-Pratt 度量",[1810,4873,4874,4877,4880],{},[1825,4875,4876],{},"2.3 常见效用函数",[1825,4878,4879],{},"不同效用函数如何影响投资比例",[1825,4881,4882],{},"CARA、CRRA、对数效用",[1810,4884,4885,4887,4890],{},[1825,4886,1851],{},[1825,4888,4889],{},"不指定效用函数时能否排序风险",[1825,4891,4892],{},"一阶与二阶随机占优",[1810,4894,4895,4898,4901],{},[1825,4896,4897],{},"2.5 确定性等价与保险",[1825,4899,4900],{},"为什么保险有正价格仍然有人买",[1825,4902,4903],{},"公平保费、风险加载、逆选择",[1800,4905,4906],{"id":4906},"常见错误与考试陷阱",[1870,4908,4909,4916,5029,5035,5041],{},[1873,4910,4911,4915],{},[4912,4913,4914],"strong",{},"把效用函数当成唯一可观测量","：效用函数本身可做正仿射变换，重要的是它代表的偏好和风险厌恶。",[1873,4917,4918,4921,4922,5028],{},[4912,4919,4920],{},"先平均财富再取效用","：风险厌恶者通常有 ",[1971,4923,4925,4967],{"className":4924},[1974],[1971,4926,4928],{"className":4927},[1978],[1980,4929,4930],{"xmlns":1982},[1984,4931,4932,4964],{},[1987,4933,4934,4936,4938,4940,4942,4944,4946,4948,4950,4952,4954,4956,4958,4960,4962],{},[1990,4935,2032],{},[2034,4937,2037],{"stretchy":2036},[1990,4939,2090],{},[2034,4941,2093],{"stretchy":2036},[1990,4943,1992],{},[2034,4945,2104],{"stretchy":2036},[2034,4947,2042],{"stretchy":2036},[2034,4949,2215],{},[1990,4951,2090],{},[2034,4953,2093],{"stretchy":2036},[1990,4955,2032],{},[2034,4957,2037],{"stretchy":2036},[1990,4959,1992],{},[2034,4961,2042],{"stretchy":2036},[2034,4963,2104],{"stretchy":2036},[1994,4965,4966],{"encoding":1996},"u(E[W])>E[u(W)]",[1971,4968,4970,5004],{"className":4969,"ariaHidden":2001},[2000],[1971,4971,4973,4976,4979,4982,4985,4988,4991,4995,4998,5001],{"className":4972},[2005],[1971,4974],{"className":4975,"style":2055},[2009],[1971,4977,2032],{"className":4978},[2014,2015],[1971,4980,2037],{"className":4981},[2062],[1971,4983,2090],{"className":4984,"style":2120},[2014,2015],[1971,4986,2093],{"className":4987},[2062],[1971,4989,1992],{"className":4990,"style":2016},[2014,2015],[1971,4992,4994],{"className":4993},[2069],"])",[1971,4996],{"className":4997,"style":2290},[2289],[1971,4999,2215],{"className":5000},[2294],[1971,5002],{"className":5003,"style":2290},[2289],[1971,5005,5007,5010,5013,5016,5019,5022,5025],{"className":5006},[2005],[1971,5008],{"className":5009,"style":2055},[2009],[1971,5011,2090],{"className":5012,"style":2120},[2014,2015],[1971,5014,2093],{"className":5015},[2062],[1971,5017,2032],{"className":5018},[2014,2015],[1971,5020,2037],{"className":5021},[2062],[1971,5023,1992],{"className":5024,"style":2016},[2014,2015],[1971,5026,2136],{"className":5027},[2069],"，顺序不能反。",[1873,5030,5031,5034],{},[4912,5032,5033],{},"混淆绝对与相对风险厌恶","：固定金额赌博和固定比例投资对应不同风险厌恶概念。",[1873,5036,5037,5040],{},[4912,5038,5039],{},"认为高方差一定更差","：若高方差资产在坏状态支付更多，可能反而像保险。",[1873,5042,5043,5046],{},[4912,5044,5045],{},"把随机占优当成均值比较","：随机占优比较的是整个分布，不只是平均值。",[1800,5048,5049],{"id":5049},"自测题",[1870,5051,5052,5055,5138,5252],{},[1873,5053,5054],{},"为什么凹效用函数意味着投资者厌恶公平赌博？",[1873,5056,5057,5058,5137],{},"对 ",[1971,5059,5061,5091],{"className":5060},[1974],[1971,5062,5064],{"className":5063},[1978],[1980,5065,5066],{"xmlns":1982},[1984,5067,5068,5088],{},[1987,5069,5070,5072,5074,5076,5078,5080,5083,5086],{},[1990,5071,2032],{},[2034,5073,2037],{"stretchy":2036},[1990,5075,1992],{},[2034,5077,2042],{"stretchy":2036},[2034,5079,2449],{},[1990,5081,5082],{},"ln",[2034,5084,5085],{},"⁡",[1990,5087,1992],{},[1994,5089,5090],{"encoding":1996},"u(W)=\\ln W",[1971,5092,5094,5121],{"className":5093,"ariaHidden":2001},[2000],[1971,5095,5097,5100,5103,5106,5109,5112,5115,5118],{"className":5096},[2005],[1971,5098],{"className":5099,"style":2055},[2009],[1971,5101,2032],{"className":5102},[2014,2015],[1971,5104,2037],{"className":5105},[2062],[1971,5107,1992],{"className":5108,"style":2016},[2014,2015],[1971,5110,2042],{"className":5111},[2069],[1971,5113],{"className":5114,"style":2290},[2289],[1971,5116,2449],{"className":5117},[2294],[1971,5119],{"className":5120,"style":2290},[2289],[1971,5122,5124,5128,5131,5134],{"className":5123},[2005],[1971,5125],{"className":5126,"style":5127},[2009],"height:0.6944em;",[1971,5129,5082],{"className":5130},[2842],[1971,5132],{"className":5133,"style":2581},[2289],[1971,5135,1992],{"className":5136,"style":2016},[2014,2015],"，判断绝对风险厌恶和相对风险厌恶随财富如何变化。",[1873,5139,5140,5141,5251],{},"某彩票 50% 概率得到 80，50% 概率得到 120，效用函数 ",[1971,5142,5144,5170],{"className":5143},[1974],[1971,5145,5147],{"className":5146},[1978],[1980,5148,5149],{"xmlns":1982},[1984,5150,5151,5167],{},[1987,5152,5153,5155,5157,5159,5161,5163],{},[1990,5154,2032],{},[2034,5156,2037],{"stretchy":2036},[1990,5158,1992],{},[2034,5160,2042],{"stretchy":2036},[2034,5162,2449],{},[4085,5164,5165],{},[1990,5166,1992],{},[1994,5168,5169],{"encoding":1996},"u(W)=\\sqrt W",[1971,5171,5173,5200],{"className":5172,"ariaHidden":2001},[2000],[1971,5174,5176,5179,5182,5185,5188,5191,5194,5197],{"className":5175},[2005],[1971,5177],{"className":5178,"style":2055},[2009],[1971,5180,2032],{"className":5181},[2014,2015],[1971,5183,2037],{"className":5184},[2062],[1971,5186,1992],{"className":5187,"style":2016},[2014,2015],[1971,5189,2042],{"className":5190},[2069],[1971,5192],{"className":5193,"style":2290},[2289],[1971,5195,2449],{"className":5196},[2294],[1971,5198],{"className":5199,"style":2290},[2289],[1971,5201,5203,5206],{"className":5202},[2005],[1971,5204],{"className":5205,"style":4128},[2009],[1971,5207,5209],{"className":5208},[2014,4132],[1971,5210,5212,5243],{"className":5211},[2246,2540],[1971,5213,5215,5240],{"className":5214},[2250],[1971,5216,5218,5228],{"className":5217,"style":4142},[2254],[1971,5219,5221,5224],{"className":5220,"style":4147},[4146],[1971,5222],{"className":5223,"style":3266},[2262],[1971,5225,1992],{"className":5226,"style":5227},[2014,2015],"margin-right:0.1389em;padding-left:0.833em;",[1971,5229,5230,5233],{"style":4160},[1971,5231],{"className":5232,"style":3266},[2262],[1971,5234,5236],{"className":5235,"style":4168},[4167],[4170,5237,5238],{"xmlns":4172,"width":4173,"height":4174,"viewBox":4175,"preserveAspectRatio":4176},[4178,5239],{"d":4180},[1971,5241,2564],{"className":5242},[2563],[1971,5244,5246],{"className":5245},[2250],[1971,5247,5249],{"className":5248,"style":4190},[2254],[1971,5250],{},"。确定性等价大约是多少？风险溢价为多少？",[1873,5253,5254],{},"一阶随机占优为什么对所有“财富越多越好”的投资者都成立？",[1800,5256,5257],{"id":5257},"答案指引",[1870,5259,5260,5369,5514,5807],{},[1873,5261,5262,5263,5368],{},"由 Jensen 不等式，凹函数满足 ",[1971,5264,5266,5308],{"className":5265},[1974],[1971,5267,5269],{"className":5268},[1978],[1980,5270,5271],{"xmlns":1982},[1984,5272,5273,5305],{},[1987,5274,5275,5277,5279,5281,5283,5285,5287,5289,5291,5293,5295,5297,5299,5301,5303],{},[1990,5276,2090],{},[2034,5278,2093],{"stretchy":2036},[1990,5280,2032],{},[2034,5282,2037],{"stretchy":2036},[1990,5284,1992],{},[2034,5286,2042],{"stretchy":2036},[2034,5288,2104],{"stretchy":2036},[2034,5290,2339],{},[1990,5292,2032],{},[2034,5294,2037],{"stretchy":2036},[1990,5296,2090],{},[2034,5298,2093],{"stretchy":2036},[1990,5300,1992],{},[2034,5302,2104],{"stretchy":2036},[2034,5304,2042],{"stretchy":2036},[1994,5306,5307],{"encoding":1996},"E[u(W)]\u003Cu(E[W])",[1971,5309,5311,5344],{"className":5310,"ariaHidden":2001},[2000],[1971,5312,5314,5317,5320,5323,5326,5329,5332,5335,5338,5341],{"className":5313},[2005],[1971,5315],{"className":5316,"style":2055},[2009],[1971,5318,2090],{"className":5319,"style":2120},[2014,2015],[1971,5321,2093],{"className":5322},[2062],[1971,5324,2032],{"className":5325},[2014,2015],[1971,5327,2037],{"className":5328},[2062],[1971,5330,1992],{"className":5331,"style":2016},[2014,2015],[1971,5333,2136],{"className":5334},[2069],[1971,5336],{"className":5337,"style":2290},[2289],[1971,5339,2339],{"className":5340},[2294],[1971,5342],{"className":5343,"style":2290},[2289],[1971,5345,5347,5350,5353,5356,5359,5362,5365],{"className":5346},[2005],[1971,5348],{"className":5349,"style":2055},[2009],[1971,5351,2032],{"className":5352},[2014,2015],[1971,5354,2037],{"className":5355},[2062],[1971,5357,2090],{"className":5358,"style":2120},[2014,2015],[1971,5360,2093],{"className":5361},[2062],[1971,5363,1992],{"className":5364,"style":2016},[2014,2015],[1971,5366,4994],{"className":5367},[2069],"。公平赌博的期望财富等于初始财富，但期望效用更低。",[1873,5370,5371,5446,5447,5513],{},[1971,5372,5374,5403],{"className":5373},[1974],[1971,5375,5377],{"className":5376},[1978],[1980,5378,5379],{"xmlns":1982},[1984,5380,5381,5400],{},[1987,5382,5383,5385,5387,5389,5391,5393,5395,5398],{},[1990,5384,3150],{},[2034,5386,2037],{"stretchy":2036},[1990,5388,1992],{},[2034,5390,2042],{"stretchy":2036},[2034,5392,2449],{},[2217,5394,2459],{},[1990,5396,5397],{"mathvariant":2204},"\u002F",[1990,5399,1992],{},[1994,5401,5402],{"encoding":1996},"A(W)=1\u002FW",[1971,5404,5406,5433],{"className":5405,"ariaHidden":2001},[2000],[1971,5407,5409,5412,5415,5418,5421,5424,5427,5430],{"className":5408},[2005],[1971,5410],{"className":5411,"style":2055},[2009],[1971,5413,3150],{"className":5414},[2014,2015],[1971,5416,2037],{"className":5417},[2062],[1971,5419,1992],{"className":5420,"style":2016},[2014,2015],[1971,5422,2042],{"className":5423},[2069],[1971,5425],{"className":5426,"style":2290},[2289],[1971,5428,2449],{"className":5429},[2294],[1971,5431],{"className":5432,"style":2290},[2289],[1971,5434,5436,5439,5443],{"className":5435},[2005],[1971,5437],{"className":5438,"style":2055},[2009],[1971,5440,5442],{"className":5441},[2014],"1\u002F",[1971,5444,1992],{"className":5445,"style":2016},[2014,2015],"，随财富上升下降；",[1971,5448,5450,5474],{"className":5449},[1974],[1971,5451,5453],{"className":5452},[1978],[1980,5454,5455],{"xmlns":1982},[1984,5456,5457,5471],{},[1987,5458,5459,5461,5463,5465,5467,5469],{},[1990,5460,3409],{},[2034,5462,2037],{"stretchy":2036},[1990,5464,1992],{},[2034,5466,2042],{"stretchy":2036},[2034,5468,2449],{},[2217,5470,2459],{},[1994,5472,5473],{"encoding":1996},"R(W)=1",[1971,5475,5477,5504],{"className":5476,"ariaHidden":2001},[2000],[1971,5478,5480,5483,5486,5489,5492,5495,5498,5501],{"className":5479},[2005],[1971,5481],{"className":5482,"style":2055},[2009],[1971,5484,3409],{"className":5485,"style":3471},[2014,2015],[1971,5487,2037],{"className":5488},[2062],[1971,5490,1992],{"className":5491,"style":2016},[2014,2015],[1971,5493,2042],{"className":5494},[2069],[1971,5496],{"className":5497,"style":2290},[2289],[1971,5499,2449],{"className":5500},[2294],[1971,5502],{"className":5503,"style":2290},[2289],[1971,5505,5507,5510],{"className":5506},[2005],[1971,5508],{"className":5509,"style":2304},[2009],[1971,5511,2459],{"className":5512},[2014],"，保持不变。这就是对数效用的常相对风险厌恶性质。",[1873,5515,5516,5748,5749,5806],{},[1971,5517,5519,5569],{"className":5518},[1974],[1971,5520,5522],{"className":5521},[1978],[1980,5523,5524],{"xmlns":1982},[1984,5525,5526,5566],{},[1987,5527,5528,5530,5532,5534,5536,5538,5540,5542,5544,5546,5551,5553,5555,5560,5563],{},[1990,5529,2090],{},[2034,5531,2093],{"stretchy":2036},[1990,5533,2032],{},[2034,5535,2037],{"stretchy":2036},[1990,5537,1992],{},[2034,5539,2042],{"stretchy":2036},[2034,5541,2104],{"stretchy":2036},[2034,5543,2449],{},[2217,5545,4224],{},[4085,5547,5548],{},[2217,5549,5550],{},"80",[2034,5552,4233],{},[2217,5554,4224],{},[4085,5556,5557],{},[2217,5558,5559],{},"120",[2034,5561,5562],{},"≈",[2217,5564,5565],{},"9.944",[1994,5567,5568],{"encoding":1996},"E[u(W)]=0.5\\sqrt{80}+0.5\\sqrt{120}\\approx9.944",[1971,5570,5572,5605,5674,5739],{"className":5571,"ariaHidden":2001},[2000],[1971,5573,5575,5578,5581,5584,5587,5590,5593,5596,5599,5602],{"className":5574},[2005],[1971,5576],{"className":5577,"style":2055},[2009],[1971,5579,2090],{"className":5580,"style":2120},[2014,2015],[1971,5582,2093],{"className":5583},[2062],[1971,5585,2032],{"className":5586},[2014,2015],[1971,5588,2037],{"className":5589},[2062],[1971,5591,1992],{"className":5592,"style":2016},[2014,2015],[1971,5594,2136],{"className":5595},[2069],[1971,5597],{"className":5598,"style":2290},[2289],[1971,5600,2449],{"className":5601},[2294],[1971,5603],{"className":5604,"style":2290},[2289],[1971,5606,5608,5612,5615,5665,5668,5671],{"className":5607},[2005],[1971,5609],{"className":5610,"style":5611},[2009],"height:1.04em;vertical-align:-0.1328em;",[1971,5613,4224],{"className":5614},[2014],[1971,5616,5618],{"className":5617},[2014,4132],[1971,5619,5621,5656],{"className":5620},[2246,2540],[1971,5622,5624,5653],{"className":5623},[2250],[1971,5625,5628,5640],{"className":5626,"style":5627},[2254],"height:0.9072em;",[1971,5629,5631,5634],{"className":5630,"style":4147},[4146],[1971,5632],{"className":5633,"style":3266},[2262],[1971,5635,5637],{"className":5636,"style":4154},[2014],[1971,5638,5550],{"className":5639},[2014],[1971,5641,5643,5646],{"style":5642},"top:-2.8672em;",[1971,5644],{"className":5645,"style":3266},[2262],[1971,5647,5649],{"className":5648,"style":4168},[4167],[4170,5650,5651],{"xmlns":4172,"width":4173,"height":4174,"viewBox":4175,"preserveAspectRatio":4176},[4178,5652],{"d":4180},[1971,5654,2564],{"className":5655},[2563],[1971,5657,5659],{"className":5658},[2250],[1971,5660,5663],{"className":5661,"style":5662},[2254],"height:0.1328em;",[1971,5664],{},[1971,5666],{"className":5667,"style":3964},[2289],[1971,5669,4233],{"className":5670},[3968],[1971,5672],{"className":5673,"style":3964},[2289],[1971,5675,5677,5680,5683,5730,5733,5736],{"className":5676},[2005],[1971,5678],{"className":5679,"style":5611},[2009],[1971,5681,4224],{"className":5682},[2014],[1971,5684,5686],{"className":5685},[2014,4132],[1971,5687,5689,5722],{"className":5688},[2246,2540],[1971,5690,5692,5719],{"className":5691},[2250],[1971,5693,5695,5707],{"className":5694,"style":5627},[2254],[1971,5696,5698,5701],{"className":5697,"style":4147},[4146],[1971,5699],{"className":5700,"style":3266},[2262],[1971,5702,5704],{"className":5703,"style":4154},[2014],[1971,5705,5559],{"className":5706},[2014],[1971,5708,5709,5712],{"style":5642},[1971,5710],{"className":5711,"style":3266},[2262],[1971,5713,5715],{"className":5714,"style":4168},[4167],[4170,5716,5717],{"xmlns":4172,"width":4173,"height":4174,"viewBox":4175,"preserveAspectRatio":4176},[4178,5718],{"d":4180},[1971,5720,2564],{"className":5721},[2563],[1971,5723,5725],{"className":5724},[2250],[1971,5726,5728],{"className":5727,"style":5662},[2254],[1971,5729],{},[1971,5731],{"className":5732,"style":2290},[2289],[1971,5734,5562],{"className":5735},[2294],[1971,5737],{"className":5738,"style":2290},[2289],[1971,5740,5742,5745],{"className":5741},[2005],[1971,5743],{"className":5744,"style":2304},[2009],[1971,5746,5565],{"className":5747},[2014],"，所以 ",[1971,5750,5752,5773],{"className":5751},[1974],[1971,5753,5755],{"className":5754},[1978],[1980,5756,5757],{"xmlns":1982},[1984,5758,5759,5770],{},[1987,5760,5761,5763,5765,5767],{},[1990,5762,3753],{},[1990,5764,2090],{},[2034,5766,5562],{},[2217,5768,5769],{},"98.9",[1994,5771,5772],{"encoding":1996},"CE\\approx98.9",[1971,5774,5776,5797],{"className":5775,"ariaHidden":2001},[2000],[1971,5777,5779,5782,5785,5788,5791,5794],{"className":5778},[2005],[1971,5780],{"className":5781,"style":2010},[2009],[1971,5783,3753],{"className":5784,"style":3771},[2014,2015],[1971,5786,2090],{"className":5787,"style":2120},[2014,2015],[1971,5789],{"className":5790,"style":2290},[2289],[1971,5792,5562],{"className":5793},[2294],[1971,5795],{"className":5796,"style":2290},[2289],[1971,5798,5800,5803],{"className":5799},[2005],[1971,5801],{"className":5802,"style":2304},[2009],[1971,5804,5769],{"className":5805},[2014],"。期望财富为 100，风险溢价约 1.1。",[1873,5808,5809],{},"一阶随机占优意味着在任意财富门槛上，一个分布至少同样可能达到更高结果，并在某些地方严格更好；只要效用单调递增，期望效用就不会更低。",[1800,5811,5812],{"id":5812},"小结与过渡",[1793,5814,5815],{},"本章把风险偏好放进资产定价：投资者关心的是状态中的效用，而不是单纯的平均金额。下一章会把这种偏好简化为均值和方差两个维度，进入马科维茨投资组合理论，并解释为什么分散化可以降低无补偿风险。",{"title":10,"searchDepth":5817,"depth":5817,"links":5818},2,[5819,5820,5821,5822,5823,5830,5831,5832,5833,5834,5835,5836],{"id":1802,"depth":5817,"text":1802},{"id":1865,"depth":5817,"text":1865},{"id":1911,"depth":5817,"text":1911},{"id":1966,"depth":5817,"text":1966},{"id":2424,"depth":5817,"text":2424,"children":5824},[5825,5827,5828,5829],{"id":2428,"depth":5826,"text":2428},3,{"id":3011,"depth":5826,"text":3011},{"id":3128,"depth":5826,"text":3129},{"id":3735,"depth":5826,"text":3735},{"id":4057,"depth":5817,"text":4058},{"id":4816,"depth":5817,"text":4817},{"id":4832,"depth":5817,"text":4832},{"id":4906,"depth":5817,"text":4906},{"id":5049,"depth":5817,"text":5049},{"id":5257,"depth":5817,"text":5257},{"id":5812,"depth":5817,"text":5812},"期望效用理论、风险厌恶与资产选择","md",{"sidebar":5840},{"order":5817},true,{"title":1260,"description":5837},"pWA2dkcNo1VAeGFW1WGRTfxmYofuYRvetPq8VXFVzRE",[5845,5847],{"title":1254,"path":1255,"stem":1256,"description":5846,"children":-1},"资产定价的基本概念与金融市场基础",{"title":1266,"path":1267,"stem":1268,"description":5848,"children":-1},"马科维茨投资组合理论与资产配置",1785754745957]