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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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Probability","\u002Fzh\u002Fprob-and-stats\u002F01-probability","zh\u002Fprob-and-stats\u002F01-probability",[1650,1656,1662,1668,1674],{"title":1651,"path":1652,"stem":1653,"children":1654},"第一章：概率论基础","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory","zh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory\u002Findex",[1655],{"title":1651,"path":1652,"stem":1653},{"title":1657,"path":1658,"stem":1659,"children":1660},"第二章：随机变量与分布","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables","zh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables\u002Findex",[1661],{"title":1657,"path":1658,"stem":1659},{"title":1663,"path":1664,"stem":1665,"children":1666},"第三章：期望、方差与条件矩","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F03-moment","zh\u002Fprob-and-stats\u002F01-probability\u002F03-moment\u002Findex",[1667],{"title":1663,"path":1664,"stem":1665},{"title":1669,"path":1670,"stem":1671,"children":1672},"第四章：常见分布族与建模机制","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F04-families","zh\u002Fprob-and-stats\u002F01-probability\u002F04-families\u002Findex",[1673],{"title":1669,"path":1670,"stem":1671},{"title":1675,"path":1676,"stem":1677,"children":1678},"第五章：收敛与渐近理论","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics","zh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics\u002Findex",[1679],{"title":1675,"path":1676,"stem":1677},{"title":1681,"path":1682,"stem":1683,"children":1684,"page":249},"02 Statistics","\u002Fzh\u002Fprob-and-stats\u002F02-statistics","zh\u002Fprob-and-stats\u002F02-statistics",[1685,1691,1697,1703,1709,1715,1721],{"title":1686,"path":1687,"stem":1688,"children":1689},"第六章：抽样分布","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling","zh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling\u002Findex",[1690],{"title":1686,"path":1687,"stem":1688},{"title":1692,"path":1693,"stem":1694,"children":1695},"第七章：区间估计","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex",[1696],{"title":1692,"path":1693,"stem":1694},{"title":1698,"path":1699,"stem":1700,"children":1701},"第八章：点估计理论","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation\u002Findex",[1702],{"title":1698,"path":1699,"stem":1700},{"title":1704,"path":1705,"stem":1706,"children":1707},"第九章：点估计方法","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method\u002Findex",[1708],{"title":1704,"path":1705,"stem":1706},{"title":1710,"path":1711,"stem":1712,"children":1713},"第十章：假设检验原理","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis","zh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis\u002Findex",[1714],{"title":1710,"path":1711,"stem":1712},{"title":1716,"path":1717,"stem":1718,"children":1719},"第十一章：常用检验方法与选择","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method\u002Findex",[1720],{"title":1716,"path":1717,"stem":1718},{"title":1722,"path":1723,"stem":1724,"children":1725},"第十二章：Bootstrap 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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",{"path":1567},{"id":1784,"title":739,"body":1785,"description":5476,"extension":5477,"features":5478,"hero":5478,"layout":5478,"locale":5478,"meta":5479,"navigation":5478,"path":740,"published":5480,"seo":5481,"stem":741,"__hash__":5482},"docs\u002Fen\u002Fmicroeconomics\u002F03-uncertainty\u002Findex.md",{"type":1786,"value":1787,"toc":5457},"minimark",[1788,1792,1797,1801,1805,1808,1827,1831,1847,2143,2159,2162,2180,2183,2187,2194,2309,2312,2419,2434,2439,2446,2833,2836,3002,3005,3009,3012,3507,3518,3701,3773,3776,3780,3801,3945,4126,4132,4345,4352,4356,4371,4374,4634,4641,4720,4727,4732,4736,4748,5074,5077,5321,5324,5328,5354,5357,5361,5371,5374,5386,5393,5397,5426,5430,5447],[1789,1790,739],"h1",{"id":1791},"module-3-choice-under-risk-and-insurance",[1793,1794,1796],"h2",{"id":1795},"core-question","Core question",[1798,1799,1800],"p",{},"How should a decision-maker compare uncertain outcomes, and when does transferring risk through insurance create value?",[1793,1802,1804],{"id":1803},"learning-outcomes","Learning outcomes",[1798,1806,1807],{},"You will be able to:",[1809,1810,1811,1815,1818,1821,1824],"ul",{},[1812,1813,1814],"li",{},"represent a lottery with expected utility and state its key assumptions;",[1812,1816,1817],{},"calculate certainty equivalents, risk premia, and Arrow–Pratt risk aversion;",[1812,1819,1820],{},"derive benchmark insurance and portfolio conditions;",[1812,1822,1823],{},"distinguish risk, ambiguity, adverse selection, and moral hazard;",[1812,1825,1826],{},"use climate-insurance evidence to identify where the benchmark is incomplete.",[1793,1828,1830],{"id":1829},"_1-outcomes-probabilities-and-timing","1. Outcomes, probabilities, and timing",[1798,1832,1833,1834,1838,1839,1842,1843,1846],{},"A lottery ",[1835,1836,1837],"code",{},"L=(p₁,x₁;…;pₙ,xₙ)"," pays outcome ",[1835,1840,1841],{},"x_s"," with probability ",[1835,1844,1845],{},"p_s",". Expected utility is:",[1848,1849,1852],"span",{"className":1850},[1851],"katex-display",[1848,1853,1856,1928],{"className":1854},[1855],"katex",[1848,1857,1860],{"className":1858},[1859],"katex-mathml",[1861,1862,1865],"math",{"xmlns":1863,"display":1864},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1866,1867,1868,1923],"semantics",{},[1869,1870,1871,1875,1880,1883,1886,1889,1898,1905,1908,1910,1917,1919],"mrow",{},[1872,1873,1874],"mi",{},"U",[1876,1877,1879],"mo",{"stretchy":1878},"false","(",[1872,1881,1882],{},"L",[1876,1884,1885],{"stretchy":1878},")",[1876,1887,1888],{},"=",[1890,1891,1892,1895],"munder",{},[1876,1893,1894],{},"∑",[1872,1896,1897],{},"s",[1899,1900,1901,1903],"msub",{},[1872,1902,1798],{},[1872,1904,1897],{},[1872,1906,1907],{},"u",[1876,1909,1879],{"stretchy":1878},[1899,1911,1912,1915],{},[1872,1913,1914],{},"x",[1872,1916,1897],{},[1876,1918,1885],{"stretchy":1878},[1872,1920,1922],{"mathvariant":1921},"normal",".",[1924,1925,1927],"annotation",{"encoding":1926},"application\u002Fx-tex","U(L)=\\sum_s p_su(x_s).",[1848,1929,1933,1971],{"className":1930,"ariaHidden":1932},[1931],"katex-html","true",[1848,1934,1937,1942,1948,1952,1955,1959,1964,1968],{"className":1935},[1936],"base",[1848,1938],{"className":1939,"style":1941},[1940],"strut","height:1em;vertical-align:-0.25em;",[1848,1943,1874],{"className":1944,"style":1947},[1945,1946],"mord","mathnormal","margin-right:0.109em;",[1848,1949,1879],{"className":1950},[1951],"mopen",[1848,1953,1882],{"className":1954},[1945,1946],[1848,1956,1885],{"className":1957},[1958],"mclose",[1848,1960],{"className":1961,"style":1963},[1962],"mspace","margin-right:0.2778em;",[1848,1965,1888],{"className":1966},[1967],"mrel",[1848,1969],{"className":1970,"style":1963},[1962],[1848,1972,1974,1978,2042,2046,2091,2094,2097,2137,2140],{"className":1973},[1936],[1848,1975],{"className":1976,"style":1977},[1940],"height:2.3em;vertical-align:-1.25em;",[1848,1979,1983],{"className":1980},[1981,1982],"mop","op-limits",[1848,1984,1988,2033],{"className":1985},[1986,1987],"vlist-t","vlist-t2",[1848,1989,1992,2028],{"className":1990},[1991],"vlist-r",[1848,1993,1997,2015],{"className":1994,"style":1996},[1995],"vlist","height:1.05em;",[1848,1998,2000,2005],{"style":1999},"top:-1.9em;margin-left:0em;",[1848,2001],{"className":2002,"style":2004},[2003],"pstrut","height:3.05em;",[1848,2006,2012],{"className":2007},[2008,2009,2010,2011],"sizing","reset-size6","size3","mtight",[1848,2013,1897],{"className":2014},[1945,1946,2011],[1848,2016,2018,2021],{"style":2017},"top:-3.05em;",[1848,2019],{"className":2020,"style":2004},[2003],[1848,2022,2023],{},[1848,2024,1894],{"className":2025},[1981,2026,2027],"op-symbol","large-op",[1848,2029,2032],{"className":2030},[2031],"vlist-s","​",[1848,2034,2036],{"className":2035},[1991],[1848,2037,2040],{"className":2038,"style":2039},[1995],"height:1.25em;",[1848,2041],{},[1848,2043],{"className":2044,"style":2045},[1962],"margin-right:0.1667em;",[1848,2047,2049,2052],{"className":2048},[1945],[1848,2050,1798],{"className":2051},[1945,1946],[1848,2053,2056],{"className":2054},[2055],"msupsub",[1848,2057,2059,2082],{"className":2058},[1986,1987],[1848,2060,2062,2079],{"className":2061},[1991],[1848,2063,2066],{"className":2064,"style":2065},[1995],"height:0.1514em;",[1848,2067,2069,2073],{"style":2068},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1848,2070],{"className":2071,"style":2072},[2003],"height:2.7em;",[1848,2074,2076],{"className":2075},[2008,2009,2010,2011],[1848,2077,1897],{"className":2078},[1945,1946,2011],[1848,2080,2032],{"className":2081},[2031],[1848,2083,2085],{"className":2084},[1991],[1848,2086,2089],{"className":2087,"style":2088},[1995],"height:0.15em;",[1848,2090],{},[1848,2092,1907],{"className":2093},[1945,1946],[1848,2095,1879],{"className":2096},[1951],[1848,2098,2100,2103],{"className":2099},[1945],[1848,2101,1914],{"className":2102},[1945,1946],[1848,2104,2106],{"className":2105},[2055],[1848,2107,2109,2129],{"className":2108},[1986,1987],[1848,2110,2112,2126],{"className":2111},[1991],[1848,2113,2115],{"className":2114,"style":2065},[1995],[1848,2116,2117,2120],{"style":2068},[1848,2118],{"className":2119,"style":2072},[2003],[1848,2121,2123],{"className":2122},[2008,2009,2010,2011],[1848,2124,1897],{"className":2125},[1945,1946,2011],[1848,2127,2032],{"className":2128},[2031],[1848,2130,2132],{"className":2131},[1991],[1848,2133,2135],{"className":2134,"style":2088},[1995],[1848,2136],{},[1848,2138,1885],{"className":2139},[1958],[1848,2141,1922],{"className":2142},[1945],[1798,2144,2145,2146,2150,2151,2154,2155,2158],{},"The von Neumann–Morgenstern representation follows from completeness, transitivity, continuity, and ",[2147,2148,2149],"strong",{},"independence"," over lotteries. Unlike ordinary ordinal utility, expected-utility representations are unique only up to a positive affine transformation ",[1835,2152,2153],{},"a+bu",", ",[1835,2156,2157],{},"b>0","; an arbitrary monotone transformation changes attitudes toward lotteries.",[1798,2160,2161],{},"Expected utility separates:",[1809,2163,2164,2170,2175],{},[1812,2165,2166,2167,2169],{},"beliefs about states, ",[1835,2168,1845],{},";",[1812,2171,2172,2173,2169],{},"consequences in each state, ",[1835,2174,1841],{},[1812,2176,2177,2178,1922],{},"utility curvature over consequences, ",[1835,2179,1907],{},[1798,2181,2182],{},"Confusing these makes “risk aversion” absorb bad information, distorted beliefs, liquidity constraints, or market frictions.",[1793,2184,2186],{"id":2185},"_2-certainty-equivalent-and-risk-premium","2. Certainty equivalent and risk premium",[1798,2188,2189,2190,2193],{},"The certainty equivalent ",[1835,2191,2192],{},"CE"," solves:",[1848,2195,2197],{"className":2196},[1851],[1848,2198,2200,2245],{"className":2199},[1855],[1848,2201,2203],{"className":2202},[1859],[1861,2204,2205],{"xmlns":1863,"display":1864},[1866,2206,2207,2242],{},[1869,2208,2209,2211,2213,2216,2219,2221,2223,2225,2228,2230,2232,2235,2237,2240],{},[1872,2210,1907],{},[1876,2212,1879],{"stretchy":1878},[1872,2214,2215],{},"C",[1872,2217,2218],{},"E",[1876,2220,1885],{"stretchy":1878},[1876,2222,1888],{},[1872,2224,2218],{},[1876,2226,2227],{"stretchy":1878},"[",[1872,2229,1907],{},[1876,2231,1879],{"stretchy":1878},[1872,2233,2234],{},"X",[1876,2236,1885],{"stretchy":1878},[1876,2238,2239],{"stretchy":1878},"]",[1872,2241,1922],{"mathvariant":1921},[1924,2243,2244],{"encoding":1926},"u(CE)=E[u(X)].",[1848,2246,2248,2280],{"className":2247,"ariaHidden":1932},[1931],[1848,2249,2251,2254,2257,2260,2264,2268,2271,2274,2277],{"className":2250},[1936],[1848,2252],{"className":2253,"style":1941},[1940],[1848,2255,1907],{"className":2256},[1945,1946],[1848,2258,1879],{"className":2259},[1951],[1848,2261,2215],{"className":2262,"style":2263},[1945,1946],"margin-right:0.0715em;",[1848,2265,2218],{"className":2266,"style":2267},[1945,1946],"margin-right:0.0576em;",[1848,2269,1885],{"className":2270},[1958],[1848,2272],{"className":2273,"style":1963},[1962],[1848,2275,1888],{"className":2276},[1967],[1848,2278],{"className":2279,"style":1963},[1962],[1848,2281,2283,2286,2289,2292,2295,2298,2302,2306],{"className":2282},[1936],[1848,2284],{"className":2285,"style":1941},[1940],[1848,2287,2218],{"className":2288,"style":2267},[1945,1946],[1848,2290,2227],{"className":2291},[1951],[1848,2293,1907],{"className":2294},[1945,1946],[1848,2296,1879],{"className":2297},[1951],[1848,2299,2234],{"className":2300,"style":2301},[1945,1946],"margin-right:0.0785em;",[1848,2303,2305],{"className":2304},[1958],")]",[1848,2307,1922],{"className":2308},[1945],[1798,2310,2311],{},"The risk premium is:",[1848,2313,2315],{"className":2314},[1851],[1848,2316,2318,2352],{"className":2317},[1855],[1848,2319,2321],{"className":2320},[1859],[1861,2322,2323],{"xmlns":1863,"display":1864},[1866,2324,2325,2349],{},[1869,2326,2327,2330,2332,2334,2336,2338,2340,2343,2345,2347],{},[1872,2328,2329],{},"ρ",[1876,2331,1888],{},[1872,2333,2218],{},[1876,2335,2227],{"stretchy":1878},[1872,2337,2234],{},[1876,2339,2239],{"stretchy":1878},[1876,2341,2342],{},"−",[1872,2344,2215],{},[1872,2346,2218],{},[1872,2348,1922],{"mathvariant":1921},[1924,2350,2351],{"encoding":1926},"\\rho=E[X]-CE.",[1848,2353,2355,2374,2403],{"className":2354,"ariaHidden":1932},[1931],[1848,2356,2358,2362,2365,2368,2371],{"className":2357},[1936],[1848,2359],{"className":2360,"style":2361},[1940],"height:0.625em;vertical-align:-0.1944em;",[1848,2363,2329],{"className":2364},[1945,1946],[1848,2366],{"className":2367,"style":1963},[1962],[1848,2369,1888],{"className":2370},[1967],[1848,2372],{"className":2373,"style":1963},[1962],[1848,2375,2377,2380,2383,2386,2389,2392,2396,2400],{"className":2376},[1936],[1848,2378],{"className":2379,"style":1941},[1940],[1848,2381,2218],{"className":2382,"style":2267},[1945,1946],[1848,2384,2227],{"className":2385},[1951],[1848,2387,2234],{"className":2388,"style":2301},[1945,1946],[1848,2390,2239],{"className":2391},[1958],[1848,2393],{"className":2394,"style":2395},[1962],"margin-right:0.2222em;",[1848,2397,2342],{"className":2398},[2399],"mbin",[1848,2401],{"className":2402,"style":2395},[1962],[1848,2404,2406,2410,2413,2416],{"className":2405},[1936],[1848,2407],{"className":2408,"style":2409},[1940],"height:0.6833em;",[1848,2411,2215],{"className":2412,"style":2263},[1945,1946],[1848,2414,2218],{"className":2415,"style":2267},[1945,1946],[1848,2417,1922],{"className":2418},[1945],[1798,2420,2421,2422,2425,2426,2429,2430,2433],{},"If ",[1835,2423,2424],{},"u''\u003C0",", Jensen's inequality gives ",[1835,2427,2428],{},"u(E[X])>E[u(X)]",", so ",[1835,2431,2432],{},"ρ>0"," for a non-degenerate risk.",[2435,2436,2438],"h3",{"id":2437},"worked-lottery","Worked lottery",[1798,2440,2441,2442,2445],{},"Initial wealth is 100. With equal probability, wealth becomes 120 or 80. Let ",[1835,2443,2444],{},"u(w)=√w",":",[1848,2447,2449],{"className":2448},[1851],[1848,2450,2452,2512],{"className":2451},[1855],[1848,2453,2455],{"className":2454},[1859],[1861,2456,2457],{"xmlns":1863,"display":1864},[1866,2458,2459,2509],{},[1869,2460,2461,2463,2465,2467,2481,2487,2490,2498,2503,2506],{},[1872,2462,2218],{},[1872,2464,1874],{},[1876,2466,1888],{},[2468,2469,2471],"mstyle",{"scriptlevel":2470,"displaystyle":1878},"0",[2472,2473,2474,2478],"mfrac",{},[2475,2476,2477],"mn",{},"1",[2475,2479,2480],{},"2",[2482,2483,2484],"msqrt",{},[2475,2485,2486],{},"120",[1876,2488,2489],{},"+",[2468,2491,2492],{"scriptlevel":2470,"displaystyle":1878},[2472,2493,2494,2496],{},[2475,2495,2477],{},[2475,2497,2480],{},[2482,2499,2500],{},[2475,2501,2502],{},"80",[1876,2504,2505],{},"≈",[2475,2507,2508],{},"9.949.",[1924,2510,2511],{"encoding":1926},"EU=\\tfrac12\\sqrt{120}+\\tfrac12\\sqrt{80}\\approx9.949.",[1848,2513,2515,2536,2693,2823],{"className":2514,"ariaHidden":1932},[1931],[1848,2516,2518,2521,2524,2527,2530,2533],{"className":2517},[1936],[1848,2519],{"className":2520,"style":2409},[1940],[1848,2522,2218],{"className":2523,"style":2267},[1945,1946],[1848,2525,1874],{"className":2526,"style":1947},[1945,1946],[1848,2528],{"className":2529,"style":1963},[1962],[1848,2531,1888],{"className":2532},[1967],[1848,2534],{"className":2535,"style":1963},[1962],[1848,2537,2539,2543,2620,2684,2687,2690],{"className":2538},[1936],[1848,2540],{"className":2541,"style":2542},[1940],"height:1.3011em;vertical-align:-0.345em;",[1848,2544,2546,2550,2617],{"className":2545},[1945],[1848,2547],{"className":2548},[1951,2549],"nulldelimiter",[1848,2551,2553],{"className":2552},[2472],[1848,2554,2556,2608],{"className":2555},[1986,1987],[1848,2557,2559,2605],{"className":2558},[1991],[1848,2560,2563,2579,2590],{"className":2561,"style":2562},[1995],"height:0.8451em;",[1848,2564,2566,2570],{"style":2565},"top:-2.655em;",[1848,2567],{"className":2568,"style":2569},[2003],"height:3em;",[1848,2571,2573],{"className":2572},[2008,2009,2010,2011],[1848,2574,2576],{"className":2575},[1945,2011],[1848,2577,2480],{"className":2578},[1945,2011],[1848,2580,2582,2585],{"style":2581},"top:-3.23em;",[1848,2583],{"className":2584,"style":2569},[2003],[1848,2586],{"className":2587,"style":2589},[2588],"frac-line","border-bottom-width:0.04em;",[1848,2591,2593,2596],{"style":2592},"top:-3.394em;",[1848,2594],{"className":2595,"style":2569},[2003],[1848,2597,2599],{"className":2598},[2008,2009,2010,2011],[1848,2600,2602],{"className":2601},[1945,2011],[1848,2603,2477],{"className":2604},[1945,2011],[1848,2606,2032],{"className":2607},[2031],[1848,2609,2611],{"className":2610},[1991],[1848,2612,2615],{"className":2613,"style":2614},[1995],"height:0.345em;",[1848,2616],{},[1848,2618],{"className":2619},[1958,2549],[1848,2621,2624],{"className":2622},[1945,2623],"sqrt",[1848,2625,2627,2675],{"className":2626},[1986,1987],[1848,2628,2630,2672],{"className":2629},[1991],[1848,2631,2634,2649],{"className":2632,"style":2633},[1995],"height:0.9561em;",[1848,2635,2639,2642],{"className":2636,"style":2638},[2637],"svg-align","top:-3em;",[1848,2640],{"className":2641,"style":2569},[2003],[1848,2643,2646],{"className":2644,"style":2645},[1945],"padding-left:0.833em;",[1848,2647,2486],{"className":2648},[1945],[1848,2650,2652,2655],{"style":2651},"top:-2.9161em;",[1848,2653],{"className":2654,"style":2569},[2003],[1848,2656,2660],{"className":2657,"style":2659},[2658],"hide-tail","min-width:0.853em;height:1.08em;",[2661,2662,2668],"svg",{"xmlns":2663,"width":2664,"height":2665,"viewBox":2666,"preserveAspectRatio":2667},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2669,2670],"path",{"d":2671},"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 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lottery's expected wealth is 100, yet the agent would exchange it for about 98.99 with certainty.",[1793,3006,3008],{"id":3007},"_3-measure-local-risk-aversion","3. Measure local risk aversion",[1798,3010,3011],{},"Absolute and relative risk aversion are:",[1848,3013,3015],{"className":3014},[1851],[1848,3016,3018,3135],{"className":3017},[1855],[1848,3019,3021],{"className":3020},[1859],[1861,3022,3023],{"xmlns":1863,"display":1864},[1866,3024,3025,3132],{},[1869,3026,3027,3030,3032,3035,3037,3039,3041,3077,3079,3081,3084,3086,3088,3090,3092,3094,3130],{},[1872,3028,3029],{},"A",[1876,3031,1879],{"stretchy":1878},[1872,3033,3034],{},"w",[1876,3036,1885],{"stretchy":1878},[1876,3038,1888],{},[1876,3040,2342],{},[2472,3042,3043,3062],{},[1869,3044,3045,3056,3058,3060],{},[2860,3046,3047,3049],{},[1872,3048,1907],{},[1869,3050,3051,3054],{},[1876,3052,3053],{"mathvariant":1921},"′",[1876,3055,3053],{"mathvariant":1921},[1876,3057,1879],{"stretchy":1878},[1872,3059,3034],{},[1876,3061,1885],{"stretchy":1878},[1869,3063,3064,3071,3073,3075],{},[2860,3065,3066,3068],{},[1872,3067,1907],{},[1876,3069,3053],{"mathvariant":1921,"lspace":3070,"rspace":3070},"0em",[1876,3072,1879],{"stretchy":1878},[1872,3074,3034],{},[1876,3076,1885],{"stretchy":1878},[1876,3078,2873],{"separator":1932},[1962,3080],{"width":2876},[1872,3082,3083],{},"R",[1876,3085,1879],{"stretchy":1878},[1872,3087,3034],{},[1876,3089,1885],{"stretchy":1878},[1876,3091,1888],{},[1876,3093,2342],{},[2472,3095,3096,3116],{},[1869,3097,3098,3100,3110,3112,3114],{},[1872,3099,3034],{},[2860,3101,3102,3104],{},[1872,3103,1907],{},[1869,3105,3106,3108],{},[1876,3107,3053],{"mathvariant":1921},[1876,3109,3053],{"mathvariant":1921},[1876,3111,1879],{"stretchy":1878},[1872,3113,3034],{},[1876,3115,1885],{"stretchy":1878},[1869,3117,3118,3124,3126,3128],{},[2860,3119,3120,3122],{},[1872,3121,1907],{},[1876,3123,3053],{"mathvariant":1921,"lspace":3070,"rspace":3070},[1876,3125,1879],{"stretchy":1878},[1872,3127,3034],{},[1876,3129,1885],{"stretchy":1878},[1872,3131,1922],{"mathvariant":1921},[1924,3133,3134],{"encoding":1926},"A(w)=-\\frac{u''(w)}{u'(w)},\n\\qquad\nR(w)=-\\frac{wu''(w)}{u'(w)}.",[1848,3136,3138,3166,3354],{"className":3137,"ariaHidden":1932},[1931],[1848,3139,3141,3144,3147,3150,3154,3157,3160,3163],{"className":3140},[1936],[1848,3142],{"className":3143,"style":1941},[1940],[1848,3145,3029],{"className":3146},[1945,1946],[1848,3148,1879],{"className":3149},[1951],[1848,3151,3034],{"className":3152,"style":3153},[1945,1946],"margin-right:0.0269em;",[1848,3155,1885],{"className":3156},[1958],[1848,3158],{"className":3159,"style":1963},[1962],[1848,3161,1888],{"className":3162},[1967],[1848,3164],{"className":3165,"style":1963},[1962],[1848,3167,3169,3173,3176,3323,3326,3329,3332,3336,3339,3342,3345,3348,3351],{"className":3168},[1936],[1848,3170],{"className":3171,"style":3172},[1940],"height:2.3649em;vertical-align:-0.936em;",[1848,3174,2342],{"className":3175},[1945],[1848,3177,3179,3182,3320],{"className":3178},[1945],[1848,3180],{"className":3181},[1951,2549],[1848,3183,3185],{"className":3184},[2472],[1848,3186,3188,3311],{"className":3187},[1986,1987],[1848,3189,3191,3308],{"className":3190},[1991],[1848,3192,3195,3247,3255],{"className":3193,"style":3194},[1995],"height:1.4289em;",[1848,3196,3198,3201],{"style":3197},"top:-2.314em;",[1848,3199],{"className":3200,"style":2569},[2003],[1848,3202,3204,3238,3241,3244],{"className":3203},[1945],[1848,3205,3207,3210],{"className":3206},[1945],[1848,3208,1907],{"className":3209},[1945,1946],[1848,3211,3213],{"className":3212},[2055],[1848,3214,3216],{"className":3215},[1986],[1848,3217,3219],{"className":3218},[1991],[1848,3220,3223],{"className":3221,"style":3222},[1995],"height:0.6779em;",[1848,3224,3226,3229],{"style":3225},"top:-2.989em;margin-right:0.05em;",[1848,3227],{"className":3228,"style":2072},[2003],[1848,3230,3232],{"className":3231},[2008,2009,2010,2011],[1848,3233,3235],{"className":3234},[1945,2011],[1848,3236,3053],{"className":3237},[1945,2011],[1848,3239,1879],{"className":3240},[1951],[1848,3242,3034],{"className":3243,"style":3153},[1945,1946],[1848,3245,1885],{"className":3246},[1958],[1848,3248,3249,3252],{"style":2581},[1848,3250],{"className":3251,"style":2569},[2003],[1848,3253],{"className":3254,"style":2589},[2588],[1848,3256,3258,3261],{"style":3257},"top:-3.677em;",[1848,3259],{"className":3260,"style":2569},[2003],[1848,3262,3264,3299,3302,3305],{"className":3263},[1945],[1848,3265,3267,3270],{"className":3266},[1945],[1848,3268,1907],{"className":3269},[1945,1946],[1848,3271,3273],{"className":3272},[2055],[1848,3274,3276],{"className":3275},[1986],[1848,3277,3279],{"className":3278},[1991],[1848,3280,3283],{"className":3281,"style":3282},[1995],"height:0.7519em;",[1848,3284,3286,3289],{"style":3285},"top:-3.063em;margin-right:0.05em;",[1848,3287],{"className":3288,"style":2072},[2003],[1848,3290,3292],{"className":3291},[2008,2009,2010,2011],[1848,3293,3295],{"className":3294},[1945,2011],[1848,3296,3298],{"className":3297},[1945,2011],"′′",[1848,3300,1879],{"className":3301},[1951],[1848,3303,3034],{"className":3304,"style":3153},[1945,1946],[1848,3306,1885],{"className":3307},[1958],[1848,3309,2032],{"className":3310},[2031],[1848,3312,3314],{"className":3313},[1991],[1848,3315,3318],{"className":3316,"style":3317},[1995],"height:0.936em;",[1848,3319],{},[1848,3321],{"className":3322},[1958,2549],[1848,3324,2873],{"className":3325},[2973],[1848,3327],{"className":3328,"style":2977},[1962],[1848,3330],{"className":3331,"style":2045},[1962],[1848,3333,3083],{"className":3334,"style":3335},[1945,1946],"margin-right:0.0077em;",[1848,3337,1879],{"className":3338},[1951],[1848,3340,3034],{"className":3341,"style":3153},[1945,1946],[1848,3343,1885],{"className":3344},[1958],[1848,3346],{"className":3347,"style":1963},[1962],[1848,3349,1888],{"className":3350},[1967],[1848,3352],{"className":3353,"style":1963},[1962],[1848,3355,3357,3360,3363,3504],{"className":3356},[1936],[1848,3358],{"className":3359,"style":3172},[1940],[1848,3361,2342],{"className":3362},[1945],[1848,3364,3366,3369,3501],{"className":3365},[1945],[1848,3367],{"className":3368},[1951,2549],[1848,3370,3372],{"className":3371},[2472],[1848,3373,3375,3493],{"className":3374},[1986,1987],[1848,3376,3378,3490],{"className":3377},[1991],[1848,3379,3381,3430,3438],{"className":3380,"style":3194},[1995],[1848,3382,3383,3386],{"style":3197},[1848,3384],{"className":3385,"style":2569},[2003],[1848,3387,3389,3421,3424,3427],{"className":3388},[1945],[1848,3390,3392,3395],{"className":3391},[1945],[1848,3393,1907],{"className":3394},[1945,1946],[1848,3396,3398],{"className":3397},[2055],[1848,3399,3401],{"className":3400},[1986],[1848,3402,3404],{"className":3403},[1991],[1848,3405,3407],{"className":3406,"style":3222},[1995],[1848,3408,3409,3412],{"style":3225},[1848,3410],{"className":3411,"style":2072},[2003],[1848,3413,3415],{"className":3414},[2008,2009,2010,2011],[1848,3416,3418],{"className":3417},[1945,2011],[1848,3419,3053],{"className":3420},[1945,2011],[1848,3422,1879],{"className":3423},[1951],[1848,3425,3034],{"className":3426,"style":3153},[1945,1946],[1848,3428,1885],{"className":3429},[1958],[1848,3431,3432,3435],{"style":2581},[1848,3433],{"className":3434,"style":2569},[2003],[1848,3436],{"className":3437,"style":2589},[2588],[1848,3439,3440,3443],{"style":3257},[1848,3441],{"className":3442,"style":2569},[2003],[1848,3444,3446,3449,3481,3484,3487],{"className":3445},[1945],[1848,3447,3034],{"className":3448,"style":3153},[1945,1946],[1848,3450,3452,3455],{"className":3451},[1945],[1848,3453,1907],{"className":3454},[1945,1946],[1848,3456,3458],{"className":3457},[2055],[1848,3459,3461],{"className":3460},[1986],[1848,3462,3464],{"className":3463},[1991],[1848,3465,3467],{"className":3466,"style":3282},[1995],[1848,3468,3469,3472],{"style":3285},[1848,3470],{"className":3471,"style":2072},[2003],[1848,3473,3475],{"className":3474},[2008,2009,2010,2011],[1848,3476,3478],{"className":3477},[1945,2011],[1848,3479,3298],{"className":3480},[1945,2011],[1848,3482,1879],{"className":3483},[1951],[1848,3485,3034],{"className":3486,"style":3153},[1945,1946],[1848,3488,1885],{"className":3489},[1958],[1848,3491,2032],{"className":3492},[2031],[1848,3494,3496],{"className":3495},[1991],[1848,3497,3499],{"className":3498,"style":3317},[1995],[1848,3500],{},[1848,3502],{"className":3503},[1958,2549],[1848,3505,1922],{"className":3506},[1945],[1798,3508,3509,3510,3513,3514,3517],{},"For a small zero-mean risk ",[1835,3511,3512],{},"ε"," with variance ",[1835,3515,3516],{},"σ²",", a second-order approximation gives:",[1848,3519,3521],{"className":3520},[1851],[1848,3522,3524,3563],{"className":3523},[1855],[1848,3525,3527],{"className":3526},[1859],[1861,3528,3529],{"xmlns":1863,"display":1864},[1866,3530,3531,3560],{},[1869,3532,3533,3535,3537,3543,3545,3547,3549,3551,3558],{},[1872,3534,2329],{},[1876,3536,2505],{},[2472,3538,3539,3541],{},[2475,3540,2477],{},[2475,3542,2480],{},[1872,3544,3029],{},[1876,3546,1879],{"stretchy":1878},[1872,3548,3034],{},[1876,3550,1885],{"stretchy":1878},[2860,3552,3553,3556],{},[1872,3554,3555],{},"σ",[2475,3557,2480],{},[1872,3559,1922],{"mathvariant":1921},[1924,3561,3562],{"encoding":1926},"\\rho\\approx\\frac12A(w)\\sigma^2.",[1848,3564,3566,3585],{"className":3565,"ariaHidden":1932},[1931],[1848,3567,3569,3573,3576,3579,3582],{"className":3568},[1936],[1848,3570],{"className":3571,"style":3572},[1940],"height:0.6776em;vertical-align:-0.1944em;",[1848,3574,2329],{"className":3575},[1945,1946],[1848,3577],{"className":3578,"style":1963},[1962],[1848,3580,2505],{"className":3581},[1967],[1848,3583],{"className":3584,"style":1963},[1962],[1848,3586,3588,3592,3656,3659,3662,3665,3668,3698],{"className":3587},[1936],[1848,3589],{"className":3590,"style":3591},[1940],"height:2.0074em;vertical-align:-0.686em;",[1848,3593,3595,3598,3653],{"className":3594},[1945],[1848,3596],{"className":3597},[1951,2549],[1848,3599,3601],{"className":3600},[2472],[1848,3602,3604,3644],{"className":3603},[1986,1987],[1848,3605,3607,3641],{"className":3606},[1991],[1848,3608,3611,3622,3630],{"className":3609,"style":3610},[1995],"height:1.3214em;",[1848,3612,3613,3616],{"style":3197},[1848,3614],{"className":3615,"style":2569},[2003],[1848,3617,3619],{"className":3618},[1945],[1848,3620,2480],{"className":3621},[1945],[1848,3623,3624,3627],{"style":2581},[1848,3625],{"className":3626,"style":2569},[2003],[1848,3628],{"className":3629,"style":2589},[2588],[1848,3631,3632,3635],{"style":3257},[1848,3633],{"className":3634,"style":2569},[2003],[1848,3636,3638],{"className":3637},[1945],[1848,3639,2477],{"className":3640},[1945],[1848,3642,2032],{"className":3643},[2031],[1848,3645,3647],{"className":3646},[1991],[1848,3648,3651],{"className":3649,"style":3650},[1995],"height:0.686em;",[1848,3652],{},[1848,3654],{"className":3655},[1958,2549],[1848,3657,3029],{"className":3658},[1945,1946],[1848,3660,1879],{"className":3661},[1951],[1848,3663,3034],{"className":3664,"style":3153},[1945,1946],[1848,3666,1885],{"className":3667},[1958],[1848,3669,3671,3675],{"className":3670},[1945],[1848,3672,3555],{"className":3673,"style":3674},[1945,1946],"margin-right:0.0359em;",[1848,3676,3678],{"className":3677},[2055],[1848,3679,3681],{"className":3680},[1986],[1848,3682,3684],{"className":3683},[1991],[1848,3685,3687],{"className":3686,"style":2917},[1995],[1848,3688,3689,3692],{"style":2941},[1848,3690],{"className":3691,"style":2072},[2003],[1848,3693,3695],{"className":3694},[2008,2009,2010,2011],[1848,3696,2480],{"className":3697},[1945,2011],[1848,3699,1922],{"className":3700},[1945],[3702,3703,3704,3720],"table",{},[3705,3706,3707],"thead",{},[3708,3709,3710,3714,3717],"tr",{},[3711,3712,3713],"th",{},"Utility",[3711,3715,3716],{},"Absolute risk aversion",[3711,3718,3719],{},"Relative risk aversion",[3721,3722,3723,3742,3756],"tbody",{},[3708,3724,3725,3731,3737],{},[3726,3727,3728],"td",{},[1835,3729,3730],{},"−e^{−aw}",[3726,3732,3733,3734],{},"constant ",[1835,3735,3736],{},"a",[3726,3738,3739],{},[1835,3740,3741],{},"aw",[3708,3743,3744,3749,3754],{},[3726,3745,3746],{},[1835,3747,3748],{},"ln w",[3726,3750,3751],{},[1835,3752,3753],{},"1\u002Fw",[3726,3755,2477],{},[3708,3757,3758,3763,3768],{},[3726,3759,3760],{},[1835,3761,3762],{},"w^{1−γ}\u002F(1−γ)",[3726,3764,3765],{},[1835,3766,3767],{},"γ\u002Fw",[3726,3769,3733,3770],{},[1835,3771,3772],{},"γ",[1798,3774,3775],{},"This is a local comparison. Two utilities can rank small risks similarly and large, skewed risks differently.",[1793,3777,3779],{"id":3778},"_4-insurance-as-state-contingent-consumption","4. Insurance as state-contingent consumption",[1798,3781,3782,3783,3786,3787,3789,3790,3792,3793,3796,3797,3800],{},"Let wealth be ",[1835,3784,3785],{},"W",", loss ",[1835,3788,1882],{}," occur with probability ",[1835,3791,1798],{},", indemnity be ",[1835,3794,3795],{},"I",", and premium ",[1835,3798,3799],{},"π(I)",". Consumption is:",[1848,3802,3804],{"className":3803},[1851],[1848,3805,3807,3844],{"className":3806},[1855],[1848,3808,3810],{"className":3809},[1859],[1861,3811,3812],{"xmlns":1863,"display":1864},[1866,3813,3814,3841],{},[1869,3815,3816,3824,3826,3828,3830,3833,3835,3837,3839],{},[1899,3817,3818,3821],{},[1872,3819,3820],{},"c",[1872,3822,3823],{},"N",[1876,3825,1888],{},[1872,3827,3785],{},[1876,3829,2342],{},[1872,3831,3832],{},"π",[1876,3834,1879],{"stretchy":1878},[1872,3836,3795],{},[1876,3838,1885],{"stretchy":1878},[1876,3840,2873],{"separator":1932},[1924,3842,3843],{"encoding":1926},"c_N=W-\\pi(I),",[1848,3845,3847,3904,3924],{"className":3846,"ariaHidden":1932},[1931],[1848,3848,3850,3854,3895,3898,3901],{"className":3849},[1936],[1848,3851],{"className":3852,"style":3853},[1940],"height:0.5806em;vertical-align:-0.15em;",[1848,3855,3857,3860],{"className":3856},[1945],[1848,3858,3820],{"className":3859},[1945,1946],[1848,3861,3863],{"className":3862},[2055],[1848,3864,3866,3887],{"className":3865},[1986,1987],[1848,3867,3869,3884],{"className":3868},[1991],[1848,3870,3873],{"className":3871,"style":3872},[1995],"height:0.3283em;",[1848,3874,3875,3878],{"style":2068},[1848,3876],{"className":3877,"style":2072},[2003],[1848,3879,3881],{"className":3880},[2008,2009,2010,2011],[1848,3882,3823],{"className":3883,"style":1947},[1945,1946,2011],[1848,3885,2032],{"className":3886},[2031],[1848,3888,3890],{"className":3889},[1991],[1848,3891,3893],{"className":3892,"style":2088},[1995],[1848,3894],{},[1848,3896],{"className":3897,"style":1963},[1962],[1848,3899,1888],{"className":3900},[1967],[1848,3902],{"className":3903,"style":1963},[1962],[1848,3905,3907,3911,3915,3918,3921],{"className":3906},[1936],[1848,3908],{"className":3909,"style":3910},[1940],"height:0.7667em;vertical-align:-0.0833em;",[1848,3912,3785],{"className":3913,"style":3914},[1945,1946],"margin-right:0.1389em;",[1848,3916],{"className":3917,"style":2395},[1962],[1848,3919,2342],{"className":3920},[2399],[1848,3922],{"className":3923,"style":2395},[1962],[1848,3925,3927,3930,3933,3936,3939,3942],{"className":3926},[1936],[1848,3928],{"className":3929,"style":1941},[1940],[1848,3931,3832],{"className":3932,"style":3674},[1945,1946],[1848,3934,1879],{"className":3935},[1951],[1848,3937,3795],{"className":3938,"style":2301},[1945,1946],[1848,3940,1885],{"className":3941},[1958],[1848,3943,2873],{"className":3944},[2973],[1848,3946,3948],{"className":3947},[1851],[1848,3949,3951,3993],{"className":3950},[1855],[1848,3952,3954],{"className":3953},[1859],[1861,3955,3956],{"xmlns":1863,"display":1864},[1866,3957,3958,3990],{},[1869,3959,3960,3966,3968,3970,3972,3974,3976,3978,3980,3982,3984,3986,3988],{},[1899,3961,3962,3964],{},[1872,3963,3820],{},[1872,3965,1882],{},[1876,3967,1888],{},[1872,3969,3785],{},[1876,3971,2342],{},[1872,3973,1882],{},[1876,3975,2489],{},[1872,3977,3795],{},[1876,3979,2342],{},[1872,3981,3832],{},[1876,3983,1879],{"stretchy":1878},[1872,3985,3795],{},[1876,3987,1885],{"stretchy":1878},[1872,3989,1922],{"mathvariant":1921},[1924,3991,3992],{"encoding":1926},"c_L=W-L+I-\\pi(I).",[1848,3994,3996,4051,4069,4087,4105],{"className":3995,"ariaHidden":1932},[1931],[1848,3997,3999,4002,4042,4045,4048],{"className":3998},[1936],[1848,4000],{"className":4001,"style":3853},[1940],[1848,4003,4005,4008],{"className":4004},[1945],[1848,4006,3820],{"className":4007},[1945,1946],[1848,4009,4011],{"className":4010},[2055],[1848,4012,4014,4034],{"className":4013},[1986,1987],[1848,4015,4017,4031],{"className":4016},[1991],[1848,4018,4020],{"className":4019,"style":3872},[1995],[1848,4021,4022,4025],{"style":2068},[1848,4023],{"className":4024,"style":2072},[2003],[1848,4026,4028],{"className":4027},[2008,2009,2010,2011],[1848,4029,1882],{"className":4030},[1945,1946,2011],[1848,4032,2032],{"className":4033},[2031],[1848,4035,4037],{"className":4036},[1991],[1848,4038,4040],{"className":4039,"style":2088},[1995],[1848,4041],{},[1848,4043],{"className":4044,"style":1963},[1962],[1848,4046,1888],{"className":4047},[1967],[1848,4049],{"className":4050,"style":1963},[1962],[1848,4052,4054,4057,4060,4063,4066],{"className":4053},[1936],[1848,4055],{"className":4056,"style":3910},[1940],[1848,4058,3785],{"className":4059,"style":3914},[1945,1946],[1848,4061],{"className":4062,"style":2395},[1962],[1848,4064,2342],{"className":4065},[2399],[1848,4067],{"className":4068,"style":2395},[1962],[1848,4070,4072,4075,4078,4081,4084],{"className":4071},[1936],[1848,4073],{"className":4074,"style":3910},[1940],[1848,4076,1882],{"className":4077},[1945,1946],[1848,4079],{"className":4080,"style":2395},[1962],[1848,4082,2489],{"className":4083},[2399],[1848,4085],{"className":4086,"style":2395},[1962],[1848,4088,4090,4093,4096,4099,4102],{"className":4089},[1936],[1848,4091],{"className":4092,"style":3910},[1940],[1848,4094,3795],{"className":4095,"style":2301},[1945,1946],[1848,4097],{"className":4098,"style":2395},[1962],[1848,4100,2342],{"className":4101},[2399],[1848,4103],{"className":4104,"style":2395},[1962],[1848,4106,4108,4111,4114,4117,4120,4123],{"className":4107},[1936],[1848,4109],{"className":4110,"style":1941},[1940],[1848,4112,3832],{"className":4113,"style":3674},[1945,1946],[1848,4115,1879],{"className":4116},[1951],[1848,4118,3795],{"className":4119,"style":2301},[1945,1946],[1848,4121,1885],{"className":4122},[1958],[1848,4124,1922],{"className":4125},[1945],[1798,4127,4128,4129,4131],{},"The consumer chooses ",[1835,4130,3795],{}," to maximise:",[1848,4133,4135],{"className":4134},[1851],[1848,4136,4138,4190],{"className":4137},[1855],[1848,4139,4141],{"className":4140},[1859],[1861,4142,4143],{"xmlns":1863,"display":1864},[1866,4144,4145,4187],{},[1869,4146,4147,4149,4151,4153,4155,4157,4159,4161,4167,4169,4171,4173,4175,4177,4183,4185],{},[1876,4148,1879],{"stretchy":1878},[2475,4150,2477],{},[1876,4152,2342],{},[1872,4154,1798],{},[1876,4156,1885],{"stretchy":1878},[1872,4158,1907],{},[1876,4160,1879],{"stretchy":1878},[1899,4162,4163,4165],{},[1872,4164,3820],{},[1872,4166,3823],{},[1876,4168,1885],{"stretchy":1878},[1876,4170,2489],{},[1872,4172,1798],{},[1872,4174,1907],{},[1876,4176,1879],{"stretchy":1878},[1899,4178,4179,4181],{},[1872,4180,3820],{},[1872,4182,1882],{},[1876,4184,1885],{"stretchy":1878},[1872,4186,1922],{"mathvariant":1921},[1924,4188,4189],{"encoding":1926},"(1-p)u(c_N)+pu(c_L).",[1848,4191,4193,4214,4284],{"className":4192,"ariaHidden":1932},[1931],[1848,4194,4196,4199,4202,4205,4208,4211],{"className":4195},[1936],[1848,4197],{"className":4198,"style":1941},[1940],[1848,4200,1879],{"className":4201},[1951],[1848,4203,2477],{"className":4204},[1945],[1848,4206],{"className":4207,"style":2395},[1962],[1848,4209,2342],{"className":4210},[2399],[1848,4212],{"className":4213,"style":2395},[1962],[1848,4215,4217,4220,4223,4226,4229,4232,4272,4275,4278,4281],{"className":4216},[1936],[1848,4218],{"className":4219,"style":1941},[1940],[1848,4221,1798],{"className":4222},[1945,1946],[1848,4224,1885],{"className":4225},[1958],[1848,4227,1907],{"className":4228},[1945,1946],[1848,4230,1879],{"className":4231},[1951],[1848,4233,4235,4238],{"className":4234},[1945],[1848,4236,3820],{"className":4237},[1945,1946],[1848,4239,4241],{"className":4240},[2055],[1848,4242,4244,4264],{"className":4243},[1986,1987],[1848,4245,4247,4261],{"className":4246},[1991],[1848,4248,4250],{"className":4249,"style":3872},[1995],[1848,4251,4252,4255],{"style":2068},[1848,4253],{"className":4254,"style":2072},[2003],[1848,4256,4258],{"className":4257},[2008,2009,2010,2011],[1848,4259,3823],{"className":4260,"style":1947},[1945,1946,2011],[1848,4262,2032],{"className":4263},[2031],[1848,4265,4267],{"className":4266},[1991],[1848,4268,4270],{"className":4269,"style":2088},[1995],[1848,4271],{},[1848,4273,1885],{"className":4274},[1958],[1848,4276],{"className":4277,"style":2395},[1962],[1848,4279,2489],{"className":4280},[2399],[1848,4282],{"className":4283,"style":2395},[1962],[1848,4285,4287,4290,4293,4296,4299,4339,4342],{"className":4286},[1936],[1848,4288],{"className":4289,"style":1941},[1940],[1848,4291,1798],{"className":4292},[1945,1946],[1848,4294,1907],{"className":4295},[1945,1946],[1848,4297,1879],{"className":4298},[1951],[1848,4300,4302,4305],{"className":4301},[1945],[1848,4303,3820],{"className":4304},[1945,1946],[1848,4306,4308],{"className":4307},[2055],[1848,4309,4311,4331],{"className":4310},[1986,1987],[1848,4312,4314,4328],{"className":4313},[1991],[1848,4315,4317],{"className":4316,"style":3872},[1995],[1848,4318,4319,4322],{"style":2068},[1848,4320],{"className":4321,"style":2072},[2003],[1848,4323,4325],{"className":4324},[2008,2009,2010,2011],[1848,4326,1882],{"className":4327},[1945,1946,2011],[1848,4329,2032],{"className":4330},[2031],[1848,4332,4334],{"className":4333},[1991],[1848,4335,4337],{"className":4336,"style":2088},[1995],[1848,4338],{},[1848,4340,1885],{"className":4341},[1958],[1848,4343,1922],{"className":4344},[1945],[1798,4346,4347,4348,4351],{},"With concave utility, actuarially fair linear pricing ",[1835,4349,4350],{},"π=pI",", no hidden action, and no other friction, full insurance equalises consumption across states. With a loading, wealth effects, background risk, or moral hazard, partial insurance and a deductible may be optimal.",[2435,4353,4355],{"id":4354},"worked-insurance-decision","Worked insurance decision",[1798,4357,4358,4359,2154,4362,2154,4365,4368,4369,1922],{},"Let ",[1835,4360,4361],{},"W=100",[1835,4363,4364],{},"p=0.1",[1835,4366,4367],{},"L=50",", and ",[1835,4370,2444],{},[1798,4372,4373],{},"Without insurance:",[1848,4375,4377],{"className":4376},[1851],[1848,4378,4380,4427],{"className":4379},[1855],[1848,4381,4383],{"className":4382},[1859],[1861,4384,4385],{"xmlns":1863,"display":1864},[1866,4386,4387,4424],{},[1869,4388,4389,4391,4397,4399,4402,4407,4409,4412,4417,4419,4422],{},[1872,4390,2218],{},[1899,4392,4393,4395],{},[1872,4394,1874],{},[2475,4396,2470],{},[1876,4398,1888],{},[2475,4400,4401],{},"0.9",[2482,4403,4404],{},[2475,4405,4406],{},"100",[1876,4408,2489],{},[2475,4410,4411],{},"0.1",[2482,4413,4414],{},[2475,4415,4416],{},"50",[1876,4418,2505],{},[2475,4420,4421],{},"9.707",[1876,4423,2873],{"separator":1932},[1924,4425,4426],{"encoding":1926},"EU_0=0.9\\sqrt{100}+0.1\\sqrt{50}\\approx9.707,",[1848,4428,4430,4491,4557,4622],{"className":4429,"ariaHidden":1932},[1931],[1848,4431,4433,4437,4440,4482,4485,4488],{"className":4432},[1936],[1848,4434],{"className":4435,"style":4436},[1940],"height:0.8333em;vertical-align:-0.15em;",[1848,4438,2218],{"className":4439,"style":2267},[1945,1946],[1848,4441,4443,4446],{"className":4442},[1945],[1848,4444,1874],{"className":4445,"style":1947},[1945,1946],[1848,4447,4449],{"className":4448},[2055],[1848,4450,4452,4474],{"className":4451},[1986,1987],[1848,4453,4455,4471],{"className":4454},[1991],[1848,4456,4459],{"className":4457,"style":4458},[1995],"height:0.3011em;",[1848,4460,4462,4465],{"style":4461},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[1848,4463],{"className":4464,"style":2072},[2003],[1848,4466,4468],{"className":4467},[2008,2009,2010,2011],[1848,4469,2470],{"className":4470},[1945,2011],[1848,4472,2032],{"className":4473},[2031],[1848,4475,4477],{"className":4476},[1991],[1848,4478,4480],{"className":4479,"style":2088},[1995],[1848,4481],{},[1848,4483],{"className":4484,"style":1963},[1962],[1848,4486,1888],{"className":4487},[1967],[1848,4489],{"className":4490,"style":1963},[1962],[1848,4492,4494,4498,4501,4548,4551,4554],{"className":4493},[1936],[1848,4495],{"className":4496,"style":4497},[1940],"height:1.04em;vertical-align:-0.0839em;",[1848,4499,4401],{"className":4500},[1945],[1848,4502,4504],{"className":4503},[1945,2623],[1848,4505,4507,4540],{"className":4506},[1986,1987],[1848,4508,4510,4537],{"className":4509},[1991],[1848,4511,4513,4525],{"className":4512,"style":2633},[1995],[1848,4514,4516,4519],{"className":4515,"style":2638},[2637],[1848,4517],{"className":4518,"style":2569},[2003],[1848,4520,4522],{"className":4521,"style":2645},[1945],[1848,4523,4406],{"className":4524},[1945],[1848,4526,4527,4530],{"style":2651},[1848,4528],{"className":4529,"style":2569},[2003],[1848,4531,4533],{"className":4532,"style":2659},[2658],[2661,4534,4535],{"xmlns":2663,"width":2664,"height":2665,"viewBox":2666,"preserveAspectRatio":2667},[2669,4536],{"d":2671},[1848,4538,2032],{"className":4539},[2031],[1848,4541,4543],{"className":4542},[1991],[1848,4544,4546],{"className":4545,"style":2681},[1995],[1848,4547],{},[1848,4549],{"className":4550,"style":2395},[1962],[1848,4552,2489],{"className":4553},[2399],[1848,4555],{"className":4556,"style":2395},[1962],[1848,4558,4560,4563,4566,4613,4616,4619],{"className":4559},[1936],[1848,4561],{"className":4562,"style":4497},[1940],[1848,4564,4411],{"className":4565},[1945],[1848,4567,4569],{"className":4568},[1945,2623],[1848,4570,4572,4605],{"className":4571},[1986,1987],[1848,4573,4575,4602],{"className":4574},[1991],[1848,4576,4578,4590],{"className":4577,"style":2633},[1995],[1848,4579,4581,4584],{"className":4580,"style":2638},[2637],[1848,4582],{"className":4583,"style":2569},[2003],[1848,4585,4587],{"className":4586,"style":2645},[1945],[1848,4588,4416],{"className":4589},[1945],[1848,4591,4592,4595],{"style":2651},[1848,4593],{"className":4594,"style":2569},[2003],[1848,4596,4598],{"className":4597,"style":2659},[2658],[2661,4599,4600],{"xmlns":2663,"width":2664,"height":2665,"viewBox":2666,"preserveAspectRatio":2667},[2669,4601],{"d":2671},[1848,4603,2032],{"className":4604},[2031],[1848,4606,4608],{"className":4607},[1991],[1848,4609,4611],{"className":4610,"style":2681},[1995],[1848,4612],{},[1848,4614],{"className":4615,"style":1963},[1962],[1848,4617,2505],{"className":4618},[1967],[1848,4620],{"className":4621,"style":1963},[1962],[1848,4623,4625,4628,4631],{"className":4624},[1936],[1848,4626],{"className":4627,"style":2966},[1940],[1848,4629,4421],{"className":4630},[1945],[1848,4632,2873],{"className":4633},[2973],[1798,4635,4636,4637,4640],{},"so ",[1835,4638,4639],{},"CE₀≈94.24",". The most this consumer pays for full coverage is approximately:",[1848,4642,4644],{"className":4643},[1851],[1848,4645,4647,4671],{"className":4646},[1855],[1848,4648,4650],{"className":4649},[1859],[1861,4651,4652],{"xmlns":1863,"display":1864},[1866,4653,4654,4668],{},[1869,4655,4656,4658,4660,4663,4665],{},[2475,4657,4406],{},[1876,4659,2342],{},[2475,4661,4662],{},"94.24",[1876,4664,1888],{},[2475,4666,4667],{},"5.76.",[1924,4669,4670],{"encoding":1926},"100-94.24=5.76.",[1848,4672,4674,4693,4711],{"className":4673,"ariaHidden":1932},[1931],[1848,4675,4677,4681,4684,4687,4690],{"className":4676},[1936],[1848,4678],{"className":4679,"style":4680},[1940],"height:0.7278em;vertical-align:-0.0833em;",[1848,4682,4406],{"className":4683},[1945],[1848,4685],{"className":4686,"style":2395},[1962],[1848,4688,2342],{"className":4689},[2399],[1848,4691],{"className":4692,"style":2395},[1962],[1848,4694,4696,4699,4702,4705,4708],{"className":4695},[1936],[1848,4697],{"className":4698,"style":2829},[1940],[1848,4700,4662],{"className":4701},[1945],[1848,4703],{"className":4704,"style":1963},[1962],[1848,4706,1888],{"className":4707},[1967],[1848,4709],{"className":4710,"style":1963},[1962],[1848,4712,4714,4717],{"className":4713},[1936],[1848,4715],{"className":4716,"style":2829},[1940],[1848,4718,4667],{"className":4719},[1945],[1798,4721,4722,4723,4726],{},"The actuarially fair premium is ",[1835,4724,4725],{},"pL=5",", so full insurance is preferred. At a premium above about 5.76, it is not. This maximum depends on wealth, utility, loss size, and other risks—not merely the expected loss.",[4728,4729,4731],"warning",{"title":4730},"Insurance can change the risk","If prevention is hidden, more coverage may reduce care: moral hazard. If high-risk buyers know more than insurers, the pool changes with price: adverse selection. Expected-utility demand alone models neither mechanism.",[1793,4733,4735],{"id":4734},"_5-portfolio-choice","5. Portfolio choice",[1798,4737,4738,4739,4741,4742,4744,4745,2445],{},"Invest share ",[1835,4740,3736],{}," in a risky asset with return ",[1835,4743,3083],{}," and the remainder at risk-free return ",[1835,4746,4747],{},"r_f",[1848,4749,4751],{"className":4750},[1851],[1848,4752,4754,4816],{"className":4753},[1855],[1848,4755,4757],{"className":4756},[1859],[1861,4758,4759],{"xmlns":1863,"display":1864},[1866,4760,4761,4813],{},[1869,4762,4763,4769,4771,4777,4779,4781,4783,4791,4793,4795,4797,4799,4801,4807,4809,4811],{},[1899,4764,4765,4767],{},[1872,4766,3785],{},[2475,4768,2477],{},[1876,4770,1888],{},[1899,4772,4773,4775],{},[1872,4774,3785],{},[2475,4776,2470],{},[1876,4778,2227],{"stretchy":1878},[2475,4780,2477],{},[1876,4782,2489],{},[1899,4784,4785,4788],{},[1872,4786,4787],{},"r",[1872,4789,4790],{},"f",[1876,4792,2489],{},[1872,4794,3736],{},[1876,4796,1879],{"stretchy":1878},[1872,4798,3083],{},[1876,4800,2342],{},[1899,4802,4803,4805],{},[1872,4804,4787],{},[1872,4806,4790],{},[1876,4808,1885],{"stretchy":1878},[1876,4810,2239],{"stretchy":1878},[1872,4812,1922],{"mathvariant":1921},[1924,4814,4815],{"encoding":1926},"W_1=W_0[1+r_f+a(R-r_f)].",[1848,4817,4819,4875,4936,4997,5021],{"className":4818,"ariaHidden":1932},[1931],[1848,4820,4822,4825,4866,4869,4872],{"className":4821},[1936],[1848,4823],{"className":4824,"style":4436},[1940],[1848,4826,4828,4831],{"className":4827},[1945],[1848,4829,3785],{"className":4830,"style":3914},[1945,1946],[1848,4832,4834],{"className":4833},[2055],[1848,4835,4837,4858],{"className":4836},[1986,1987],[1848,4838,4840,4855],{"className":4839},[1991],[1848,4841,4843],{"className":4842,"style":4458},[1995],[1848,4844,4846,4849],{"style":4845},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1848,4847],{"className":4848,"style":2072},[2003],[1848,4850,4852],{"className":4851},[2008,2009,2010,2011],[1848,4853,2477],{"className":4854},[1945,2011],[1848,4856,2032],{"className":4857},[2031],[1848,4859,4861],{"className":4860},[1991],[1848,4862,4864],{"className":4863,"style":2088},[1995],[1848,4865],{},[1848,4867],{"className":4868,"style":1963},[1962],[1848,4870,1888],{"className":4871},[1967],[1848,4873],{"className":4874,"style":1963},[1962],[1848,4876,4878,4881,4921,4924,4927,4930,4933],{"className":4877},[1936],[1848,4879],{"className":4880,"style":1941},[1940],[1848,4882,4884,4887],{"className":4883},[1945],[1848,4885,3785],{"className":4886,"style":3914},[1945,1946],[1848,4888,4890],{"className":4889},[2055],[1848,4891,4893,4913],{"className":4892},[1986,1987],[1848,4894,4896,4910],{"className":4895},[1991],[1848,4897,4899],{"className":4898,"style":4458},[1995],[1848,4900,4901,4904],{"style":4845},[1848,4902],{"className":4903,"style":2072},[2003],[1848,4905,4907],{"className":4906},[2008,2009,2010,2011],[1848,4908,2470],{"className":4909},[1945,2011],[1848,4911,2032],{"className":4912},[2031],[1848,4914,4916],{"className":4915},[1991],[1848,4917,4919],{"className":4918,"style":2088},[1995],[1848,4920],{},[1848,4922,2227],{"className":4923},[1951],[1848,4925,2477],{"className":4926},[1945],[1848,4928],{"className":4929,"style":2395},[1962],[1848,4931,2489],{"className":4932},[2399],[1848,4934],{"className":4935,"style":2395},[1962],[1848,4937,4939,4943,4988,4991,4994],{"className":4938},[1936],[1848,4940],{"className":4941,"style":4942},[1940],"height:0.8694em;vertical-align:-0.2861em;",[1848,4944,4946,4950],{"className":4945},[1945],[1848,4947,4787],{"className":4948,"style":4949},[1945,1946],"margin-right:0.0278em;",[1848,4951,4953],{"className":4952},[2055],[1848,4954,4956,4979],{"className":4955},[1986,1987],[1848,4957,4959,4976],{"className":4958},[1991],[1848,4960,4963],{"className":4961,"style":4962},[1995],"height:0.3361em;",[1848,4964,4966,4969],{"style":4965},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1848,4967],{"className":4968,"style":2072},[2003],[1848,4970,4972],{"className":4971},[2008,2009,2010,2011],[1848,4973,4790],{"className":4974,"style":4975},[1945,1946,2011],"margin-right:0.1076em;",[1848,4977,2032],{"className":4978},[2031],[1848,4980,4982],{"className":4981},[1991],[1848,4983,4986],{"className":4984,"style":4985},[1995],"height:0.2861em;",[1848,4987],{},[1848,4989],{"className":4990,"style":2395},[1962],[1848,4992,2489],{"className":4993},[2399],[1848,4995],{"className":4996,"style":2395},[1962],[1848,4998,5000,5003,5006,5009,5012,5015,5018],{"className":4999},[1936],[1848,5001],{"className":5002,"style":1941},[1940],[1848,5004,3736],{"className":5005},[1945,1946],[1848,5007,1879],{"className":5008},[1951],[1848,5010,3083],{"className":5011,"style":3335},[1945,1946],[1848,5013],{"className":5014,"style":2395},[1962],[1848,5016,2342],{"className":5017},[2399],[1848,5019],{"className":5020,"style":2395},[1962],[1848,5022,5024,5028,5068,5071],{"className":5023},[1936],[1848,5025],{"className":5026,"style":5027},[1940],"height:1.0361em;vertical-align:-0.2861em;",[1848,5029,5031,5034],{"className":5030},[1945],[1848,5032,4787],{"className":5033,"style":4949},[1945,1946],[1848,5035,5037],{"className":5036},[2055],[1848,5038,5040,5060],{"className":5039},[1986,1987],[1848,5041,5043,5057],{"className":5042},[1991],[1848,5044,5046],{"className":5045,"style":4962},[1995],[1848,5047,5048,5051],{"style":4965},[1848,5049],{"className":5050,"style":2072},[2003],[1848,5052,5054],{"className":5053},[2008,2009,2010,2011],[1848,5055,4790],{"className":5056,"style":4975},[1945,1946,2011],[1848,5058,2032],{"className":5059},[2031],[1848,5061,5063],{"className":5062},[1991],[1848,5064,5066],{"className":5065,"style":4985},[1995],[1848,5067],{},[1848,5069,2305],{"className":5070},[1958],[1848,5072,1922],{"className":5073},[1945],[1798,5075,5076],{},"An interior optimum satisfies:",[1848,5078,5080],{"className":5079},[1851],[1848,5081,5083,5138],{"className":5082},[1855],[1848,5084,5086],{"className":5085},[1859],[1861,5087,5088],{"xmlns":1863,"display":1864},[1866,5089,5090,5135],{},[1869,5091,5092,5094,5130,5132],{},[1872,5093,2218],{},[1869,5095,5096,5098,5104,5106,5112,5114,5116,5118,5120,5126,5128],{},[1876,5097,2227],{"fence":1932},[2860,5099,5100,5102],{},[1872,5101,1907],{},[1876,5103,3053],{"mathvariant":1921,"lspace":3070,"rspace":3070},[1876,5105,1879],{"stretchy":1878},[1899,5107,5108,5110],{},[1872,5109,3785],{},[2475,5111,2477],{},[1876,5113,1885],{"stretchy":1878},[1876,5115,1879],{"stretchy":1878},[1872,5117,3083],{},[1876,5119,2342],{},[1899,5121,5122,5124],{},[1872,5123,4787],{},[1872,5125,4790],{},[1876,5127,1885],{"stretchy":1878},[1876,5129,2239],{"fence":1932},[1876,5131,1888],{},[2475,5133,5134],{},"0.",[1924,5136,5137],{"encoding":1926},"E\\left[u'(W_1)(R-r_f)\\right]=0.",[1848,5139,5141,5312],{"className":5140,"ariaHidden":1932},[1931],[1848,5142,5144,5148,5151,5154,5303,5306,5309],{"className":5143},[1936],[1848,5145],{"className":5146,"style":5147},[1940],"height:1.088em;vertical-align:-0.2861em;",[1848,5149,2218],{"className":5150,"style":2267},[1945,1946],[1848,5152],{"className":5153,"style":2045},[1962],[1848,5155,5158,5163,5196,5199,5239,5242,5245,5248,5251,5254,5257,5297,5300],{"className":5156},[5157],"minner",[1848,5159,2227],{"className":5160,"style":5162},[1951,5161],"delimcenter","top:0em;",[1848,5164,5166,5169],{"className":5165},[1945],[1848,5167,1907],{"className":5168},[1945,1946],[1848,5170,5172],{"className":5171},[2055],[1848,5173,5175],{"className":5174},[1986],[1848,5176,5178],{"className":5177},[1991],[1848,5179,5182],{"className":5180,"style":5181},[1995],"height:0.8019em;",[1848,5183,5184,5187],{"style":2941},[1848,5185],{"className":5186,"style":2072},[2003],[1848,5188,5190],{"className":5189},[2008,2009,2010,2011],[1848,5191,5193],{"className":5192},[1945,2011],[1848,5194,3053],{"className":5195},[1945,2011],[1848,5197,1879],{"className":5198},[1951],[1848,5200,5202,5205],{"className":5201},[1945],[1848,5203,3785],{"className":5204,"style":3914},[1945,1946],[1848,5206,5208],{"className":5207},[2055],[1848,5209,5211,5231],{"className":5210},[1986,1987],[1848,5212,5214,5228],{"className":5213},[1991],[1848,5215,5217],{"className":5216,"style":4458},[1995],[1848,5218,5219,5222],{"style":4845},[1848,5220],{"className":5221,"style":2072},[2003],[1848,5223,5225],{"className":5224},[2008,2009,2010,2011],[1848,5226,2477],{"className":5227},[1945,2011],[1848,5229,2032],{"className":5230},[2031],[1848,5232,5234],{"className":5233},[1991],[1848,5235,5237],{"className":5236,"style":2088},[1995],[1848,5238],{},[1848,5240,1885],{"className":5241},[1958],[1848,5243,1879],{"className":5244},[1951],[1848,5246,3083],{"className":5247,"style":3335},[1945,1946],[1848,5249],{"className":5250,"style":2395},[1962],[1848,5252,2342],{"className":5253},[2399],[1848,5255],{"className":5256,"style":2395},[1962],[1848,5258,5260,5263],{"className":5259},[1945],[1848,5261,4787],{"className":5262,"style":4949},[1945,1946],[1848,5264,5266],{"className":5265},[2055],[1848,5267,5269,5289],{"className":5268},[1986,1987],[1848,5270,5272,5286],{"className":5271},[1991],[1848,5273,5275],{"className":5274,"style":4962},[1995],[1848,5276,5277,5280],{"style":4965},[1848,5278],{"className":5279,"style":2072},[2003],[1848,5281,5283],{"className":5282},[2008,2009,2010,2011],[1848,5284,4790],{"className":5285,"style":4975},[1945,1946,2011],[1848,5287,2032],{"className":5288},[2031],[1848,5290,5292],{"className":5291},[1991],[1848,5293,5295],{"className":5294,"style":4985},[1995],[1848,5296],{},[1848,5298,1885],{"className":5299},[1958],[1848,5301,2239],{"className":5302,"style":5162},[1958,5161],[1848,5304],{"className":5305,"style":1963},[1962],[1848,5307,1888],{"className":5308},[1967],[1848,5310],{"className":5311,"style":1963},[1962],[1848,5313,5315,5318],{"className":5314},[1936],[1848,5316],{"className":5317,"style":2829},[1940],[1848,5319,5134],{"className":5320},[1945],[1798,5322,5323],{},"The expected excess return is weighted by marginal utility: losses in bad states matter more. Under quadratic\u002Fnormal approximations, higher expected return raises the risky share while variance and risk aversion lower it. With fat tails, borrowing constraints, or multiple background risks, mean and variance are insufficient.",[1793,5325,5327],{"id":5326},"_6-risk-is-not-ambiguity","6. Risk is not ambiguity",[1809,5329,5330,5336,5342,5348],{},[1812,5331,5332,5335],{},[2147,5333,5334],{},"Risk:"," probabilities are treated as known.",[1812,5337,5338,5341],{},[2147,5339,5340],{},"Ambiguity:"," probabilities or the model generating outcomes are uncertain.",[1812,5343,5344,5347],{},[2147,5345,5346],{},"Parameter uncertainty:"," probabilities are estimated with error.",[1812,5349,5350,5353],{},[2147,5351,5352],{},"Deep uncertainty:"," even relevant states or mechanisms are contested.",[1798,5355,5356],{},"Expected utility can incorporate subjective probabilities, but it does not by itself explain Ellsberg-type ambiguity aversion or probability weighting. Module 9 treats behavioural alternatives; they are competing models with their own testable restrictions, not permission to explain any anomaly after the fact.",[1793,5358,5360],{"id":5359},"_7-current-case-wildfire-risk-classification","7. Current case: wildfire-risk classification",[1798,5362,5363,5364,5370],{},"Boomhower, Fowlie, Gellman, and Plantinga combine parcel-level wildfire risk with insurer filings. Their 2024 working paper, revised in 2025, documents large differences in insurers' classification and pricing methods. Insurers using coarser risk measures can face adverse selection relative to firms with richer models, charge high prices in risky segments, or withdraw (",[3736,5365,5369],{"href":5366,"rel":5367},"https:\u002F\u002Fdoi.org\u002F10.3386\u002Fw32625",[5368],"nofollow","NBER Working Paper 32625",").",[1798,5372,5373],{},"The case links three layers:",[5375,5376,5377,5380,5383],"ol",{},[1812,5378,5379],{},"households value risk transfer through expected utility;",[1812,5381,5382],{},"insurers differ in information and classification technology;",[1812,5384,5385],{},"regulation constrains prices and participation.",[1798,5387,5388,5389,5392],{},"It does ",[2147,5390,5391],{},"not"," identify one optimal regulatory rule for every disaster market. The paper studies a particular market and uses proprietary risk data; climate trends, reinsurance, public backstops, and household adaptation also affect equilibrium.",[1793,5394,5396],{"id":5395},"practice","Practice",[5375,5398,5399,5411,5414,5420,5423],{},[1812,5400,5401,5402,5404,5405,5407,5408,1922],{},"Compute ",[1835,5403,2192],{}," and ",[1835,5406,2329],{}," for a 50–50 lottery over 64 and 144 with ",[1835,5409,5410],{},"u=√w",[1812,5412,5413],{},"Show that a risk-neutral consumer buys actuarially fair insurance but will not pay a positive loading in the benchmark.",[1812,5415,5416,5417,1922],{},"Derive the insurance first-order condition for ",[1835,5418,5419],{},"π(I)=qI",[1812,5421,5422],{},"Explain why a deductible can reduce moral hazard without eliminating insurance value.",[1812,5424,5425],{},"Separate preference, belief, information, and regulation explanations for rising wildfire premiums.",[1793,5427,5429],{"id":5428},"quick-check","Quick check",[1809,5431,5432,5435,5438,5441,5444],{},[1812,5433,5434],{},"Expected value and expected utility answer different questions.",[1812,5436,5437],{},"Utility curvature determines risk attitude only within the specified outcome domain.",[1812,5439,5440],{},"Certainty equivalents put utility comparisons back into outcome units.",[1812,5442,5443],{},"Full insurance is a benchmark requiring fair pricing and no hidden action.",[1812,5445,5446],{},"Real insurance markets combine risk preferences with information, contracts, and regulation.",[1798,5448,5449,5452,5453,1922],{},[2147,5450,5451],{},"Next:"," ",[3736,5454,5456],{"href":5455},"..\u002F04-general-equilibrium\u002F","make individual plans jointly feasible in general equilibrium",{"title":10,"searchDepth":5458,"depth":5458,"links":5459},2,[5460,5461,5462,5463,5467,5468,5471,5472,5473,5474,5475],{"id":1795,"depth":5458,"text":1796},{"id":1803,"depth":5458,"text":1804},{"id":1829,"depth":5458,"text":1830},{"id":2185,"depth":5458,"text":2186,"children":5464},[5465],{"id":2437,"depth":5466,"text":2438},3,{"id":3007,"depth":5458,"text":3008},{"id":3778,"depth":5458,"text":3779,"children":5469},[5470],{"id":4354,"depth":5466,"text":4355},{"id":4734,"depth":5458,"text":4735},{"id":5326,"depth":5458,"text":5327},{"id":5359,"depth":5458,"text":5360},{"id":5395,"depth":5458,"text":5396},{"id":5428,"depth":5458,"text":5429},"Expected utility, certainty equivalents, risk aversion, insurance, portfolio choice, ambiguity, and climate-risk evidence.","md",null,{},true,{"title":739,"description":5476},"u1AWKwWyQBIaET-hFPpCxcfvVVqcs04lq_Bt_Wr5QPA",[5484,5486],{"title":733,"path":734,"stem":735,"description":5485,"children":-1},"Implicit derivatives, Slutsky decomposition, compensating and equivalent variation, surplus, incidence, and empirical welfare.",{"title":745,"path":746,"stem":747,"description":5487,"children":-1},"Exchange economies, Walrasian equilibrium, Pareto efficiency, welfare theorems, existence, distribution, production, and network propagation.",1785754732360]