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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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First define the loss variable ",[1797,1798,1801,1823],"span",{"className":1799},[1800],"katex",[1797,1802,1805],{"className":1803},[1804],"katex-mathml",[1806,1807,1809],"math",{"xmlns":1808},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1810,1811,1812,1819],"semantics",{},[1813,1814,1815],"mrow",{},[1816,1817,1818],"mi",{},"L",[1820,1821,1818],"annotation",{"encoding":1822},"application\u002Fx-tex",[1797,1824,1828],{"className":1825,"ariaHidden":1827},[1826],"katex-html","true",[1797,1829,1832,1837],{"className":1830},[1831],"base",[1797,1833],{"className":1834,"style":1836},[1835],"strut","height:0.6833em;",[1797,1838,1818],{"className":1839},[1840,1841],"mord","mathnormal","—gross claims, net claims, underwriting loss, or change in own funds—and its horizon.",[1844,1845,1847],"h2",{"id":1846},"_1-var-and-tvar","1. VaR and TVaR",[1793,1849,1850,1851,1883],{},"At confidence level ",[1797,1852,1854,1869],{"className":1853},[1800],[1797,1855,1857],{"className":1856},[1804],[1806,1858,1859],{"xmlns":1808},[1810,1860,1861,1866],{},[1813,1862,1863],{},[1816,1864,1865],{},"α",[1820,1867,1868],{"encoding":1822},"\\alpha",[1797,1870,1872],{"className":1871,"ariaHidden":1827},[1826],[1797,1873,1875,1879],{"className":1874},[1831],[1797,1876],{"className":1877,"style":1878},[1835],"height:0.4306em;",[1797,1880,1865],{"className":1881,"style":1882},[1840,1841],"margin-right:0.0037em;",",",[1797,1885,1888],{"className":1886},[1887],"katex-display",[1797,1889,1891,1970],{"className":1890},[1800],[1797,1892,1894],{"className":1893},[1804],[1806,1895,1897],{"xmlns":1808,"display":1896},"block",[1810,1898,1899,1967],{},[1813,1900,1901,1916,1920,1922,1925,1928,1931,1933,1936,1939,1942,1945,1947,1949,1952,1954,1956,1959,1961,1964],{},[1902,1903,1904,1914],"msub",{},[1813,1905,1906,1910],{},[1816,1907,1909],{"mathvariant":1908},"normal","VaR",[1911,1912,1913],"mo",{},"⁡",[1816,1915,1865],{},[1911,1917,1919],{"stretchy":1918},"false","(",[1816,1921,1818],{},[1911,1923,1924],{"stretchy":1918},")",[1911,1926,1927],{},"=",[1816,1929,1930],{},"inf",[1911,1932,1913],{},[1911,1934,1935],{"stretchy":1918},"{",[1816,1937,1938],{},"l",[1911,1940,1941],{},":",[1816,1943,1944],{},"P",[1911,1946,1919],{"stretchy":1918},[1816,1948,1818],{},[1911,1950,1951],{},"≤",[1816,1953,1938],{},[1911,1955,1924],{"stretchy":1918},[1911,1957,1958],{},"≥",[1816,1960,1865],{},[1911,1962,1963],{"stretchy":1918},"}",[1816,1965,1966],{"mathvariant":1908},".",[1820,1968,1969],{"encoding":1822},"\\operatorname{VaR}_\\alpha(L)\n=\\inf\\{l:P(L\\le l)\\ge\\alpha\\}.",[1797,1971,1973,2064,2094,2119,2140],{"className":1972,"ariaHidden":1827},[1826],[1797,1974,1976,1980,2041,2045,2048,2052,2057,2061],{"className":1975},[1831],[1797,1977],{"className":1978,"style":1979},[1835],"height:1em;vertical-align:-0.25em;",[1797,1981,1984,1991],{"className":1982},[1983],"mop",[1797,1985,1987],{"className":1986},[1983],[1797,1988,1909],{"className":1989},[1840,1990],"mathrm",[1797,1992,1995],{"className":1993},[1994],"msupsub",[1797,1996,2000,2032],{"className":1997},[1998,1999],"vlist-t","vlist-t2",[1797,2001,2004,2027],{"className":2002},[2003],"vlist-r",[1797,2005,2009],{"className":2006,"style":2008},[2007],"vlist","height:0.1514em;",[1797,2010,2012,2017],{"style":2011},"top:-2.55em;margin-right:0.05em;",[1797,2013],{"className":2014,"style":2016},[2015],"pstrut","height:2.7em;",[1797,2018,2024],{"className":2019},[2020,2021,2022,2023],"sizing","reset-size6","size3","mtight",[1797,2025,1865],{"className":2026,"style":1882},[1840,1841,2023],[1797,2028,2031],{"className":2029},[2030],"vlist-s","​",[1797,2033,2035],{"className":2034},[2003],[1797,2036,2039],{"className":2037,"style":2038},[2007],"height:0.15em;",[1797,2040],{},[1797,2042,1919],{"className":2043},[2044],"mopen",[1797,2046,1818],{"className":2047},[1840,1841],[1797,2049,1924],{"className":2050},[2051],"mclose",[1797,2053],{"className":2054,"style":2056},[2055],"mspace","margin-right:0.2778em;",[1797,2058,1927],{"className":2059},[2060],"mrel",[1797,2062],{"className":2063,"style":2056},[2055],[1797,2065,2067,2070,2078,2081,2085,2088,2091],{"className":2066},[1831],[1797,2068],{"className":2069,"style":1979},[1835],[1797,2071,2073,2074],{"className":2072},[1983],"in",[1797,2075,2077],{"style":2076},"margin-right:0.0778em;","f",[1797,2079,1935],{"className":2080},[2044],[1797,2082,1938],{"className":2083,"style":2084},[1840,1841],"margin-right:0.0197em;",[1797,2086],{"className":2087,"style":2056},[2055],[1797,2089,1941],{"className":2090},[2060],[1797,2092],{"className":2093,"style":2056},[2055],[1797,2095,2097,2100,2104,2107,2110,2113,2116],{"className":2096},[1831],[1797,2098],{"className":2099,"style":1979},[1835],[1797,2101,1944],{"className":2102,"style":2103},[1840,1841],"margin-right:0.1389em;",[1797,2105,1919],{"className":2106},[2044],[1797,2108,1818],{"className":2109},[1840,1841],[1797,2111],{"className":2112,"style":2056},[2055],[1797,2114,1951],{"className":2115},[2060],[1797,2117],{"className":2118,"style":2056},[2055],[1797,2120,2122,2125,2128,2131,2134,2137],{"className":2121},[1831],[1797,2123],{"className":2124,"style":1979},[1835],[1797,2126,1938],{"className":2127,"style":2084},[1840,1841],[1797,2129,1924],{"className":2130},[2051],[1797,2132],{"className":2133,"style":2056},[2055],[1797,2135,1958],{"className":2136},[2060],[1797,2138],{"className":2139,"style":2056},[2055],[1797,2141,2143,2146,2149,2152],{"className":2142},[1831],[1797,2144],{"className":2145,"style":1979},[1835],[1797,2147,1865],{"className":2148,"style":1882},[1840,1841],[1797,2150,1963],{"className":2151},[2051],[1797,2153,1966],{"className":2154},[1840],[1793,2156,2157,2158,2186],{},"For a continuous loss distribution, VaR is its ",[1797,2159,2161,2174],{"className":2160},[1800],[1797,2162,2164],{"className":2163},[1804],[1806,2165,2166],{"xmlns":1808},[1810,2167,2168,2172],{},[1813,2169,2170],{},[1816,2171,1865],{},[1820,2173,1868],{"encoding":1822},[1797,2175,2177],{"className":2176,"ariaHidden":1827},[1826],[1797,2178,2180,2183],{"className":2179},[1831],[1797,2181],{"className":2182,"style":1878},[1835],[1797,2184,1865],{"className":2185,"style":1882},[1840,1841]," quantile. Tail Value at Risk is",[1797,2188,2190],{"className":2189},[1887],[1797,2191,2193,2278],{"className":2192},[1800],[1797,2194,2196],{"className":2195},[1804],[1806,2197,2198],{"xmlns":1808,"display":1896},[1810,2199,2200,2275],{},[1813,2201,2202,2213,2215,2217,2219,2221,2237,2247,2258,2260,2262,2264,2268,2271,2273],{},[1902,2203,2204,2211],{},[1813,2205,2206,2209],{},[1816,2207,2208],{"mathvariant":1908},"TVaR",[1911,2210,1913],{},[1816,2212,1865],{},[1911,2214,1919],{"stretchy":1918},[1816,2216,1818],{},[1911,2218,1924],{"stretchy":1918},[1911,2220,1927],{},[2222,2223,2224,2228],"mfrac",{},[2225,2226,2227],"mn",{},"1",[1813,2229,2230,2232,2235],{},[2225,2231,2227],{},[1911,2233,2234],{},"−",[1816,2236,1865],{},[2238,2239,2240,2243,2245],"msubsup",{},[1911,2241,2242],{},"∫",[1816,2244,1865],{},[2225,2246,2227],{},[1902,2248,2249,2255],{},[1813,2250,2251,2253],{},[1816,2252,1909],{"mathvariant":1908},[1911,2254,1913],{},[1816,2256,2257],{},"u",[1911,2259,1919],{"stretchy":1918},[1816,2261,1818],{},[1911,2263,1924],{"stretchy":1918},[2265,2266,2267],"mtext",{}," ",[1816,2269,2270],{},"d",[1816,2272,2257],{},[1816,2274,1966],{"mathvariant":1908},[1820,2276,2277],{"encoding":1822},"\\operatorname{TVaR}_\\alpha(L)\n=\\frac{1}{1-\\alpha}\\int_\\alpha^1\\operatorname{VaR}_u(L)\\,du.",[1797,2279,2281,2348],{"className":2280,"ariaHidden":1827},[1826],[1797,2282,2284,2287,2330,2333,2336,2339,2342,2345],{"className":2283},[1831],[1797,2285],{"className":2286,"style":1979},[1835],[1797,2288,2290,2296],{"className":2289},[1983],[1797,2291,2293],{"className":2292},[1983],[1797,2294,2208],{"className":2295},[1840,1990],[1797,2297,2299],{"className":2298},[1994],[1797,2300,2302,2322],{"className":2301},[1998,1999],[1797,2303,2305,2319],{"className":2304},[2003],[1797,2306,2308],{"className":2307,"style":2008},[2007],[1797,2309,2310,2313],{"style":2011},[1797,2311],{"className":2312,"style":2016},[2015],[1797,2314,2316],{"className":2315},[2020,2021,2022,2023],[1797,2317,1865],{"className":2318,"style":1882},[1840,1841,2023],[1797,2320,2031],{"className":2321},[2030],[1797,2323,2325],{"className":2324},[2003],[1797,2326,2328],{"className":2327,"style":2038},[2007],[1797,2329],{},[1797,2331,1919],{"className":2332},[2044],[1797,2334,1818],{"className":2335},[1840,1841],[1797,2337,1924],{"className":2338},[2051],[1797,2340],{"className":2341,"style":2056},[2055],[1797,2343,1927],{"className":2344},[2060],[1797,2346],{"className":2347,"style":2056},[2055],[1797,2349,2351,2355,2440,2444,2502,2505,2548,2551,2554,2557,2560,2563,2566],{"className":2350},[1831],[1797,2352],{"className":2353,"style":2354},[1835],"height:2.476em;vertical-align:-0.9119em;",[1797,2356,2358,2362,2437],{"className":2357},[1840],[1797,2359],{"className":2360},[2044,2361],"nulldelimiter",[1797,2363,2365],{"className":2364},[2222],[1797,2366,2368,2428],{"className":2367},[1998,1999],[1797,2369,2371,2425],{"className":2370},[2003],[1797,2372,2375,2402,2413],{"className":2373,"style":2374},[2007],"height:1.3214em;",[1797,2376,2378,2382],{"style":2377},"top:-2.314em;",[1797,2379],{"className":2380,"style":2381},[2015],"height:3em;",[1797,2383,2385,2388,2392,2396,2399],{"className":2384},[1840],[1797,2386,2227],{"className":2387},[1840],[1797,2389],{"className":2390,"style":2391},[2055],"margin-right:0.2222em;",[1797,2393,2234],{"className":2394},[2395],"mbin",[1797,2397],{"className":2398,"style":2391},[2055],[1797,2400,1865],{"className":2401,"style":1882},[1840,1841],[1797,2403,2405,2408],{"style":2404},"top:-3.23em;",[1797,2406],{"className":2407,"style":2381},[2015],[1797,2409],{"className":2410,"style":2412},[2411],"frac-line","border-bottom-width:0.04em;",[1797,2414,2416,2419],{"style":2415},"top:-3.677em;",[1797,2417],{"className":2418,"style":2381},[2015],[1797,2420,2422],{"className":2421},[1840],[1797,2423,2227],{"className":2424},[1840],[1797,2426,2031],{"className":2427},[2030],[1797,2429,2431],{"className":2430},[2003],[1797,2432,2435],{"className":2433,"style":2434},[2007],"height:0.7693em;",[1797,2436],{},[1797,2438],{"className":2439},[2051,2361],[1797,2441],{"className":2442,"style":2443},[2055],"margin-right:0.1667em;",[1797,2445,2447,2453],{"className":2446},[1983],[1797,2448,2242],{"className":2449,"style":2452},[1983,2450,2451],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[1797,2454,2456],{"className":2455},[1994],[1797,2457,2459,2493],{"className":2458},[1998,1999],[1797,2460,2462,2490],{"className":2461},[2003],[1797,2463,2466,2478],{"className":2464,"style":2465},[2007],"height:1.564em;",[1797,2467,2469,2472],{"style":2468},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[1797,2470],{"className":2471,"style":2016},[2015],[1797,2473,2475],{"className":2474},[2020,2021,2022,2023],[1797,2476,1865],{"className":2477,"style":1882},[1840,1841,2023],[1797,2479,2481,2484],{"style":2480},"top:-3.8129em;margin-right:0.05em;",[1797,2482],{"className":2483,"style":2016},[2015],[1797,2485,2487],{"className":2486},[2020,2021,2022,2023],[1797,2488,2227],{"className":2489},[1840,2023],[1797,2491,2031],{"className":2492},[2030],[1797,2494,2496],{"className":2495},[2003],[1797,2497,2500],{"className":2498,"style":2499},[2007],"height:0.9119em;",[1797,2501],{},[1797,2503],{"className":2504,"style":2443},[2055],[1797,2506,2508,2514],{"className":2507},[1983],[1797,2509,2511],{"className":2510},[1983],[1797,2512,1909],{"className":2513},[1840,1990],[1797,2515,2517],{"className":2516},[1994],[1797,2518,2520,2540],{"className":2519},[1998,1999],[1797,2521,2523,2537],{"className":2522},[2003],[1797,2524,2526],{"className":2525,"style":2008},[2007],[1797,2527,2528,2531],{"style":2011},[1797,2529],{"className":2530,"style":2016},[2015],[1797,2532,2534],{"className":2533},[2020,2021,2022,2023],[1797,2535,2257],{"className":2536},[1840,1841,2023],[1797,2538,2031],{"className":2539},[2030],[1797,2541,2543],{"className":2542},[2003],[1797,2544,2546],{"className":2545,"style":2038},[2007],[1797,2547],{},[1797,2549,1919],{"className":2550},[2044],[1797,2552,1818],{"className":2553},[1840,1841],[1797,2555,1924],{"className":2556},[2051],[1797,2558],{"className":2559,"style":2443},[2055],[1797,2561,2270],{"className":2562},[1840,1841],[1797,2564,2257],{"className":2565},[1840,1841],[1797,2567,1966],{"className":2568},[1840],[1793,2570,2571,2572,1966],{},"For continuous distributions it equals ",[1797,2573,2575,2622],{"className":2574},[1800],[1797,2576,2578],{"className":2577},[1804],[1806,2579,2580],{"xmlns":1808},[1810,2581,2582,2619],{},[1813,2583,2584,2587,2590,2592,2595,2597,2600,2610,2612,2614,2616],{},[1816,2585,2586],{},"E",[1911,2588,2589],{"stretchy":1918},"[",[1816,2591,1818],{},[1911,2593,2594],{},"∣",[1816,2596,1818],{},[1911,2598,2599],{},">",[1902,2601,2602,2608],{},[1813,2603,2604,2606],{},[1816,2605,1909],{"mathvariant":1908},[1911,2607,1913],{},[1816,2609,1865],{},[1911,2611,1919],{"stretchy":1918},[1816,2613,1818],{},[1911,2615,1924],{"stretchy":1918},[1911,2617,2618],{"stretchy":1918},"]",[1820,2620,2621],{"encoding":1822},"E[L\\mid L>\\operatorname{VaR}_\\alpha(L)]",[1797,2623,2625,2650,2669],{"className":2624,"ariaHidden":1827},[1826],[1797,2626,2628,2631,2635,2638,2641,2644,2647],{"className":2627},[1831],[1797,2629],{"className":2630,"style":1979},[1835],[1797,2632,2586],{"className":2633,"style":2634},[1840,1841],"margin-right:0.0576em;",[1797,2636,2589],{"className":2637},[2044],[1797,2639,1818],{"className":2640},[1840,1841],[1797,2642],{"className":2643,"style":2056},[2055],[1797,2645,2594],{"className":2646},[2060],[1797,2648],{"className":2649,"style":2056},[2055],[1797,2651,2653,2657,2660,2663,2666],{"className":2652},[1831],[1797,2654],{"className":2655,"style":2656},[1835],"height:0.7224em;vertical-align:-0.0391em;",[1797,2658,1818],{"className":2659},[1840,1841],[1797,2661],{"className":2662,"style":2056},[2055],[1797,2664,2599],{"className":2665},[2060],[1797,2667],{"className":2668,"style":2056},[2055],[1797,2670,2672,2675,2718,2721,2724],{"className":2671},[1831],[1797,2673],{"className":2674,"style":1979},[1835],[1797,2676,2678,2684],{"className":2677},[1983],[1797,2679,2681],{"className":2680},[1983],[1797,2682,1909],{"className":2683},[1840,1990],[1797,2685,2687],{"className":2686},[1994],[1797,2688,2690,2710],{"className":2689},[1998,1999],[1797,2691,2693,2707],{"className":2692},[2003],[1797,2694,2696],{"className":2695,"style":2008},[2007],[1797,2697,2698,2701],{"style":2011},[1797,2699],{"className":2700,"style":2016},[2015],[1797,2702,2704],{"className":2703},[2020,2021,2022,2023],[1797,2705,1865],{"className":2706,"style":1882},[1840,1841,2023],[1797,2708,2031],{"className":2709},[2030],[1797,2711,2713],{"className":2712},[2003],[1797,2714,2716],{"className":2715,"style":2038},[2007],[1797,2717],{},[1797,2719,1919],{"className":2720},[2044],[1797,2722,1818],{"className":2723},[1840,1841],[1797,2725,2727],{"className":2726},[2051],")]",[2729,2730,2731,2747],"table",{},[2732,2733,2734],"thead",{},[2735,2736,2737,2741,2744],"tr",{},[2738,2739,2740],"th",{},"Measure",[2738,2742,2743],{},"Reads as",[2738,2745,2746],{},"Main limitation",[2748,2749,2750,2762],"tbody",{},[2735,2751,2752,2756,2759],{},[2753,2754,2755],"td",{},"VaR 99%",[2753,2757,2758],{},"threshold exceeded in about 1% of modelled periods",[2753,2760,2761],{},"says nothing about how bad exceedances are; not generally subadditive",[2735,2763,2764,2767,2770],{},[2753,2765,2766],{},"TVaR 99%",[2753,2768,2769],{},"mean loss in the worst 1% under a continuous model",[2753,2771,2772],{},"more tail-sensitive and data\u002Fmodel hungry",[1793,2774,2775],{},"Neither is “capital” until premiums, expenses, assets, management actions, horizon, and decision rules are specified.",[1844,2777,2779],{"id":2778},"_2-empirical-estimation","2. Empirical estimation",[1793,2781,2782,2783,1941],{},"For simulated losses ",[1797,2784,2786,2818],{"className":2785},[1800],[1797,2787,2789],{"className":2788},[1804],[1806,2790,2791],{"xmlns":1808},[1810,2792,2793,2815],{},[1813,2794,2795,2801,2803,2806,2808],{},[1902,2796,2797,2799],{},[1816,2798,1818],{},[2225,2800,2227],{},[1911,2802,1883],{"separator":1827},[1911,2804,2805],{},"…",[1911,2807,1883],{"separator":1827},[1902,2809,2810,2812],{},[1816,2811,1818],{},[1816,2813,2814],{},"M",[1820,2816,2817],{"encoding":1822},"L_1,\\ldots,L_M",[1797,2819,2821],{"className":2820,"ariaHidden":1827},[1826],[1797,2822,2824,2828,2870,2874,2877,2881,2884,2887,2890],{"className":2823},[1831],[1797,2825],{"className":2826,"style":2827},[1835],"height:0.8778em;vertical-align:-0.1944em;",[1797,2829,2831,2834],{"className":2830},[1840],[1797,2832,1818],{"className":2833},[1840,1841],[1797,2835,2837],{"className":2836},[1994],[1797,2838,2840,2862],{"className":2839},[1998,1999],[1797,2841,2843,2859],{"className":2842},[2003],[1797,2844,2847],{"className":2845,"style":2846},[2007],"height:0.3011em;",[1797,2848,2850,2853],{"style":2849},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1797,2851],{"className":2852,"style":2016},[2015],[1797,2854,2856],{"className":2855},[2020,2021,2022,2023],[1797,2857,2227],{"className":2858},[1840,2023],[1797,2860,2031],{"className":2861},[2030],[1797,2863,2865],{"className":2864},[2003],[1797,2866,2868],{"className":2867,"style":2038},[2007],[1797,2869],{},[1797,2871,1883],{"className":2872},[2873],"mpunct",[1797,2875],{"className":2876,"style":2443},[2055],[1797,2878,2805],{"className":2879},[2880],"minner",[1797,2882],{"className":2883,"style":2443},[2055],[1797,2885,1883],{"className":2886},[2873],[1797,2888],{"className":2889,"style":2443},[2055],[1797,2891,2893,2896],{"className":2892},[1840],[1797,2894,1818],{"className":2895},[1840,1841],[1797,2897,2899],{"className":2898},[1994],[1797,2900,2902,2924],{"className":2901},[1998,1999],[1797,2903,2905,2921],{"className":2904},[2003],[1797,2906,2909],{"className":2907,"style":2908},[2007],"height:0.3283em;",[1797,2910,2911,2914],{"style":2849},[1797,2912],{"className":2913,"style":2016},[2015],[1797,2915,2917],{"className":2916},[2020,2021,2022,2023],[1797,2918,2814],{"className":2919,"style":2920},[1840,1841,2023],"margin-right:0.109em;",[1797,2922,2031],{"className":2923},[2030],[1797,2925,2927],{"className":2926},[2003],[1797,2928,2930],{"className":2929,"style":2038},[2007],[1797,2931],{},[2933,2934,2935,2939,2942,2945],"ol",{},[2936,2937,2938],"li",{},"sort the losses;",[2936,2940,2941],{},"use a documented quantile convention for VaR;",[2936,2943,2944],{},"average losses beyond the selected threshold for a simple continuous-sample TVaR estimate;",[2936,2946,2947,2948,3014],{},"quantify Monte Carlo error—especially when ",[1797,2949,2951,2975],{"className":2950},[1800],[1797,2952,2954],{"className":2953},[1804],[1806,2955,2956],{"xmlns":1808},[1810,2957,2958,2972],{},[1813,2959,2960,2962,2964,2966,2968,2970],{},[1911,2961,1919],{"stretchy":1918},[2225,2963,2227],{},[1911,2965,2234],{},[1816,2967,1865],{},[1911,2969,1924],{"stretchy":1918},[1816,2971,2814],{},[1820,2973,2974],{"encoding":1822},"(1-\\alpha)M",[1797,2976,2978,2999],{"className":2977,"ariaHidden":1827},[1826],[1797,2979,2981,2984,2987,2990,2993,2996],{"className":2980},[1831],[1797,2982],{"className":2983,"style":1979},[1835],[1797,2985,1919],{"className":2986},[2044],[1797,2988,2227],{"className":2989},[1840],[1797,2991],{"className":2992,"style":2391},[2055],[1797,2994,2234],{"className":2995},[2395],[1797,2997],{"className":2998,"style":2391},[2055],[1797,3000,3002,3005,3008,3011],{"className":3001},[1831],[1797,3003],{"className":3004,"style":1979},[1835],[1797,3006,1865],{"className":3007,"style":1882},[1840,1841],[1797,3009,1924],{"className":3010},[2051],[1797,3012,2814],{"className":3013,"style":2920},[1840,1841]," is small.",[1793,3016,3017],{},"At 99.5%, 10,000 simulations leave only about 50 tail observations. That is usually weak evidence for a stable TVaR.",[1844,3019,3021],{"id":3020},"_3-dependence-can-erase-apparent-diversification","3. Dependence can erase apparent diversification",[1793,3023,3024],{},"Two regions can have identical marginal count and severity models but share catastrophe states. The next experiment compares independent regional states with one shared state while preserving each region's marginal distribution.",[3026,3027],"pyodide",{"code64":3028,"layout":3029,"locale":7,"packages":3030,"title":3031},"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","vertical","numpy,pandas,matplotlib","Same marginals, different dependence",[1793,3033,3034],{},"The marginal model for each region is unchanged. Only dependence changes, yet aggregate tail risk should increase materially under the shared state.",[1844,3036,3038],{"id":3037},"_4-reinsurance-and-capital","4. Reinsurance and capital",[1793,3040,3041],{},"Calculate risk measures on the correctly transformed net loss:",[1797,3043,3045],{"className":3044},[1887],[1797,3046,3048,3100],{"className":3047},[1800],[1797,3049,3051],{"className":3050},[1804],[1806,3052,3053],{"xmlns":1808,"display":1896},[1810,3054,3055,3097],{},[1813,3056,3057,3065,3067,3074,3076,3079,3081,3087,3089,3092,3095],{},[3058,3059,3060,3062],"msup",{},[1816,3061,1818],{},[2265,3063,3064],{},"net",[1911,3066,1927],{},[3058,3068,3069,3071],{},[1816,3070,1818],{},[2265,3072,3073],{},"gross",[1911,3075,2234],{},[1816,3077,3078],{},"R",[1911,3080,1919],{"stretchy":1918},[3058,3082,3083,3085],{},[1816,3084,1818],{},[2265,3086,3073],{},[1911,3088,1924],{"stretchy":1918},[1911,3090,3091],{},"+",[2265,3093,3094],{},"reinsurance premium and costs",[1911,3096,1883],{"separator":1827},[1820,3098,3099],{"encoding":1822},"L^{\\text{net}}\n=L^{\\text{gross}}-R(L^{\\text{gross}})\n+\\text{reinsurance premium and costs},",[1797,3101,3103,3156,3208,3268],{"className":3102,"ariaHidden":1827},[1826],[1797,3104,3106,3110,3147,3150,3153],{"className":3105},[1831],[1797,3107],{"className":3108,"style":3109},[1835],"height:0.8436em;",[1797,3111,3113,3116],{"className":3112},[1840],[1797,3114,1818],{"className":3115},[1840,1841],[1797,3117,3119],{"className":3118},[1994],[1797,3120,3122],{"className":3121},[1998],[1797,3123,3125],{"className":3124},[2003],[1797,3126,3128],{"className":3127,"style":3109},[2007],[1797,3129,3131,3134],{"style":3130},"top:-3.113em;margin-right:0.05em;",[1797,3132],{"className":3133,"style":2016},[2015],[1797,3135,3137],{"className":3136},[2020,2021,2022,2023],[1797,3138,3140],{"className":3139},[1840,2023],[1797,3141,3144],{"className":3142},[1840,3143,2023],"text",[1797,3145,3064],{"className":3146},[1840,2023],[1797,3148],{"className":3149,"style":2056},[2055],[1797,3151,1927],{"className":3152},[2060],[1797,3154],{"className":3155,"style":2056},[2055],[1797,3157,3159,3163,3199,3202,3205],{"className":3158},[1831],[1797,3160],{"className":3161,"style":3162},[1835],"height:0.7977em;vertical-align:-0.0833em;",[1797,3164,3166,3169],{"className":3165},[1840],[1797,3167,1818],{"className":3168},[1840,1841],[1797,3170,3172],{"className":3171},[1994],[1797,3173,3175],{"className":3174},[1998],[1797,3176,3178],{"className":3177},[2003],[1797,3179,3182],{"className":3180,"style":3181},[2007],"height:0.7144em;",[1797,3183,3184,3187],{"style":3130},[1797,3185],{"className":3186,"style":2016},[2015],[1797,3188,3190],{"className":3189},[2020,2021,2022,2023],[1797,3191,3193],{"className":3192},[1840,2023],[1797,3194,3196],{"className":3195},[1840,3143,2023],[1797,3197,3073],{"className":3198},[1840,2023],[1797,3200],{"className":3201,"style":2391},[2055],[1797,3203,2234],{"className":3204},[2395],[1797,3206],{"className":3207,"style":2391},[2055],[1797,3209,3211,3214,3218,3221,3256,3259,3262,3265],{"className":3210},[1831],[1797,3212],{"className":3213,"style":1979},[1835],[1797,3215,3078],{"className":3216,"style":3217},[1840,1841],"margin-right:0.0077em;",[1797,3219,1919],{"className":3220},[2044],[1797,3222,3224,3227],{"className":3223},[1840],[1797,3225,1818],{"className":3226},[1840,1841],[1797,3228,3230],{"className":3229},[1994],[1797,3231,3233],{"className":3232},[1998],[1797,3234,3236],{"className":3235},[2003],[1797,3237,3239],{"className":3238,"style":3181},[2007],[1797,3240,3241,3244],{"style":3130},[1797,3242],{"className":3243,"style":2016},[2015],[1797,3245,3247],{"className":3246},[2020,2021,2022,2023],[1797,3248,3250],{"className":3249},[1840,2023],[1797,3251,3253],{"className":3252},[1840,3143,2023],[1797,3254,3073],{"className":3255},[1840,2023],[1797,3257,1924],{"className":3258},[2051],[1797,3260],{"className":3261,"style":2391},[2055],[1797,3263,3091],{"className":3264},[2395],[1797,3266],{"className":3267,"style":2391},[2055],[1797,3269,3271,3275,3281],{"className":3270},[1831],[1797,3272],{"className":3273,"style":3274},[1835],"height:0.8889em;vertical-align:-0.1944em;",[1797,3276,3278],{"className":3277},[1840,3143],[1797,3279,3094],{"className":3280},[1840],[1797,3282,1883],{"className":3283},[2873],[1793,3285,3286,3287,3315],{},"where ",[1797,3288,3290,3303],{"className":3289},[1800],[1797,3291,3293],{"className":3292},[1804],[1806,3294,3295],{"xmlns":1808},[1810,3296,3297,3301],{},[1813,3298,3299],{},[1816,3300,3078],{},[1820,3302,3078],{"encoding":1822},[1797,3304,3306],{"className":3305,"ariaHidden":1827},[1826],[1797,3307,3309,3312],{"className":3308},[1831],[1797,3310],{"className":3311,"style":1836},[1835],[1797,3313,3078],{"className":3314,"style":3217},[1840,1841]," must implement the treaty at its contract unit. Then examine:",[3317,3318,3319,3322,3325,3328,3331],"ul",{},[2936,3320,3321],{},"gross and net expected result;",[2936,3323,3324],{},"gross and net VaR\u002FTVaR;",[2936,3326,3327],{},"attachment and exhaustion probability;",[2936,3329,3330],{},"basis and counterparty scenarios;",[2936,3332,3333],{},"model sensitivity near the layer.",[1793,3335,3336],{},"Ignoring reinsurance price makes every ceded layer look beneficial.",[1844,3338,3340],{"id":3339},"_5-parameter-and-model-risk","5. Parameter and model risk",[1793,3342,3343],{},"Tail results are functions of estimated inputs:",[1797,3345,3347],{"className":3346},[1887],[1797,3348,3350,3393],{"className":3349},[1800],[1797,3351,3353],{"className":3352},[1804],[1806,3354,3355],{"xmlns":1808,"display":1896},[1810,3356,3357,3390],{},[1813,3358,3359,3362,3364,3366,3369,3378,3380,3386,3388],{},[1816,3360,3361],{},"ρ",[1911,3363,1919],{"stretchy":1918},[1816,3365,1818],{},[1911,3367,3368],{"separator":1827},";",[3370,3371,3372,3375],"mover",{"accent":1827},[1816,3373,3374],{},"θ",[1911,3376,3377],{"stretchy":1827},"^",[1911,3379,1883],{"separator":1827},[3370,3381,3382,3384],{"accent":1827},[1816,3383,2814],{},[1911,3385,3377],{"stretchy":1827},[1911,3387,1924],{"stretchy":1918},[1911,3389,1883],{"separator":1827},[1820,3391,3392],{"encoding":1822},"\\rho(L;\\widehat\\theta,\\widehat M),",[1797,3394,3396],{"className":3395,"ariaHidden":1827},[1826],[1797,3397,3399,3403,3406,3409,3412,3415,3418,3465,3468,3471,3505,3508],{"className":3398},[1831],[1797,3400],{"className":3401,"style":3402},[1835],"height:1.1844em;vertical-align:-0.25em;",[1797,3404,3361],{"className":3405},[1840,1841],[1797,3407,1919],{"className":3408},[2044],[1797,3410,1818],{"className":3411},[1840,1841],[1797,3413,3368],{"className":3414},[2873],[1797,3416],{"className":3417,"style":2443},[2055],[1797,3419,3422],{"className":3420},[1840,3421],"accent",[1797,3423,3425],{"className":3424},[1998],[1797,3426,3428],{"className":3427},[2003],[1797,3429,3432,3442],{"className":3430,"style":3431},[2007],"height:0.9344em;",[1797,3433,3435,3438],{"style":3434},"top:-3em;",[1797,3436],{"className":3437,"style":2381},[2015],[1797,3439,3374],{"className":3440,"style":3441},[1840,1841],"margin-right:0.0278em;",[1797,3443,3447,3450],{"className":3444,"style":3446},[3445],"svg-align","width:calc(100% - 0.1667em);margin-left:0.1667em;top:-3.6944em;",[1797,3448],{"className":3449,"style":2381},[2015],[1797,3451,3453],{"style":3452},"height:0.24em;",[3454,3455,3461],"svg",{"xmlns":3456,"width":3457,"height":3458,"viewBox":3459,"preserveAspectRatio":3460},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","100%","0.24em","0 0 1062 239","none",[3462,3463],"path",{"d":3464},"M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z",[1797,3466,1883],{"className":3467},[2873],[1797,3469],{"className":3470,"style":2443},[2055],[1797,3472,3474],{"className":3473},[1840,3421],[1797,3475,3477],{"className":3476},[1998],[1797,3478,3480],{"className":3479},[2003],[1797,3481,3484,3492],{"className":3482,"style":3483},[2007],"height:0.9233em;",[1797,3485,3486,3489],{"style":3434},[1797,3487],{"className":3488,"style":2381},[2015],[1797,3490,2814],{"className":3491,"style":2920},[1840,1841],[1797,3493,3496,3499],{"className":3494,"style":3495},[3445],"width:calc(100% - 0.1667em);margin-left:0.1667em;top:-3.6833em;",[1797,3497],{"className":3498,"style":2381},[2015],[1797,3500,3501],{"style":3452},[3454,3502,3503],{"xmlns":3456,"width":3457,"height":3458,"viewBox":3459,"preserveAspectRatio":3460},[3462,3504],{"d":3464},[1797,3506,1924],{"className":3507},[2051],[1797,3509,1883],{"className":3510},[2873],[1793,3512,3286,3513,3543,3544,3572],{},[1797,3514,3516,3530],{"className":3515},[1800],[1797,3517,3519],{"className":3518},[1804],[1806,3520,3521],{"xmlns":1808},[1810,3522,3523,3527],{},[1813,3524,3525],{},[1816,3526,3374],{},[1820,3528,3529],{"encoding":1822},"\\theta",[1797,3531,3533],{"className":3532,"ariaHidden":1827},[1826],[1797,3534,3536,3540],{"className":3535},[1831],[1797,3537],{"className":3538,"style":3539},[1835],"height:0.6944em;",[1797,3541,3374],{"className":3542,"style":3441},[1840,1841]," are parameters and ",[1797,3545,3547,3560],{"className":3546},[1800],[1797,3548,3550],{"className":3549},[1804],[1806,3551,3552],{"xmlns":1808},[1810,3553,3554,3558],{},[1813,3555,3556],{},[1816,3557,2814],{},[1820,3559,2814],{"encoding":1822},[1797,3561,3563],{"className":3562,"ariaHidden":1827},[1826],[1797,3564,3566,3569],{"className":3565},[1831],[1797,3567],{"className":3568,"style":1836},[1835],[1797,3570,2814],{"className":3571,"style":2920},[1840,1841]," is model structure. A professional analysis varies:",[3317,3574,3575,3578,3581,3584,3587,3590],{},[2936,3576,3577],{},"frequency trend and catastrophe rate;",[2936,3579,3580],{},"severity tail family and threshold;",[2936,3582,3583],{},"inflation and portfolio mix;",[2936,3585,3586],{},"dependence\u002Fcommon-shock structure;",[2936,3588,3589],{},"treaty wording, exhaustion, and default;",[2936,3591,3592],{},"reserve and premium uncertainty.",[1793,3594,3595],{},"Report model spread alongside simulation error. Running more simulations reduces only Monte Carlo error.",[1844,3597,3599],{"id":3598},"_6-current-catastrophe-evidence","6. Current catastrophe evidence",[1793,3601,3602],{},"Swiss Re Institute's 2025 catastrophe estimate—USD 220bn economic losses, 49% insured, and 92% of insured losses from secondary perils—motivates repeated-event and regional-dependence scenarios. It does not supply Harbour Mutual's catastrophe probability, severity tail, or correlation.",[1793,3604,3605],{},"Use event catalogues and insurer exposure to calibrate; use current publications to challenge scenario completeness.",[1844,3607,3609],{"id":3608},"_7-regulatory-boundary","7. Regulatory boundary",[1793,3611,3612],{},"Classical aggregate models and VaR\u002FTVaR are analytical building blocks. They are not, by themselves:",[3317,3614,3615,3618,3621],{},[2936,3616,3617],{},"an IFRS 17 insurance-contract measurement;",[2936,3619,3620],{},"a Solvency UK Solvency Capital Requirement;",[2936,3622,3623],{},"a complete internal model or Own Risk and Solvency Assessment.",[1793,3625,3626],{},"Solvency UK reporting applies for reporting dates from 31 December 2024, and the PRA's current supervisory statements define requirements within a broader legal and governance framework. Always verify the current rulebook and firm permissions; do not infer compliance from a classroom percentile.",[1844,3628,3630],{"id":3629},"practice","Practice",[2933,3632,3633,3837,3840],{},[2936,3634,3635,3636,3737,3738,3836],{},"A loss sample has VaR",[1797,3637,3639,3666],{"className":3638},[1800],[1797,3640,3642],{"className":3641},[1804],[1806,3643,3644],{"xmlns":1808},[1810,3645,3646,3663],{},[1813,3647,3648,3655,3657,3660],{},[1902,3649,3650,3652],{},[1813,3651],{},[2225,3653,3654],{},"99",[1911,3656,1927],{},[1816,3658,3659],{"mathvariant":1908},"£",[2225,3661,3662],{},"10",[1820,3664,3665],{"encoding":1822},"_{99}=£10",[1797,3667,3669,3727],{"className":3668,"ariaHidden":1827},[1826],[1797,3670,3672,3676,3718,3721,3724],{"className":3671},[1831],[1797,3673],{"className":3674,"style":3675},[1835],"height:0.5169em;vertical-align:-0.15em;",[1797,3677,3679,3681],{"className":3678},[1840],[1797,3680],{},[1797,3682,3684],{"className":3683},[1994],[1797,3685,3687,3710],{"className":3686},[1998,1999],[1797,3688,3690,3707],{"className":3689},[2003],[1797,3691,3693],{"className":3692,"style":2846},[2007],[1797,3694,3695,3698],{"style":2011},[1797,3696],{"className":3697,"style":2016},[2015],[1797,3699,3701],{"className":3700},[2020,2021,2022,2023],[1797,3702,3704],{"className":3703},[1840,2023],[1797,3705,3654],{"className":3706},[1840,2023],[1797,3708,2031],{"className":3709},[2030],[1797,3711,3713],{"className":3712},[2003],[1797,3714,3716],{"className":3715,"style":2038},[2007],[1797,3717],{},[1797,3719],{"className":3720,"style":2056},[2055],[1797,3722,1927],{"className":3723},[2060],[1797,3725],{"className":3726,"style":2056},[2055],[1797,3728,3730,3733],{"className":3729},[1831],[1797,3731],{"className":3732,"style":3539},[1835],[1797,3734,3736],{"className":3735},[1840],"£10","m and TVaR",[1797,3739,3741,3766],{"className":3740},[1800],[1797,3742,3744],{"className":3743},[1804],[1806,3745,3746],{"xmlns":1808},[1810,3747,3748,3763],{},[1813,3749,3750,3756,3758,3760],{},[1902,3751,3752,3754],{},[1813,3753],{},[2225,3755,3654],{},[1911,3757,1927],{},[1816,3759,3659],{"mathvariant":1908},[2225,3761,3762],{},"18",[1820,3764,3765],{"encoding":1822},"_{99}=£18",[1797,3767,3769,3826],{"className":3768,"ariaHidden":1827},[1826],[1797,3770,3772,3775,3817,3820,3823],{"className":3771},[1831],[1797,3773],{"className":3774,"style":3675},[1835],[1797,3776,3778,3780],{"className":3777},[1840],[1797,3779],{},[1797,3781,3783],{"className":3782},[1994],[1797,3784,3786,3809],{"className":3785},[1998,1999],[1797,3787,3789,3806],{"className":3788},[2003],[1797,3790,3792],{"className":3791,"style":2846},[2007],[1797,3793,3794,3797],{"style":2011},[1797,3795],{"className":3796,"style":2016},[2015],[1797,3798,3800],{"className":3799},[2020,2021,2022,2023],[1797,3801,3803],{"className":3802},[1840,2023],[1797,3804,3654],{"className":3805},[1840,2023],[1797,3807,2031],{"className":3808},[2030],[1797,3810,3812],{"className":3811},[2003],[1797,3813,3815],{"className":3814,"style":2038},[2007],[1797,3816],{},[1797,3818],{"className":3819,"style":2056},[2055],[1797,3821,1927],{"className":3822},[2060],[1797,3824],{"className":3825,"style":2056},[2055],[1797,3827,3829,3832],{"className":3828},[1831],[1797,3830],{"className":3831,"style":3539},[1835],[1797,3833,3835],{"className":3834},[1840],"£18","m. Explain the difference in one sentence.",[2936,3838,3839],{},"Why does doubling simulations not solve tail-model uncertainty?",[2936,3841,3842],{},"Two portfolios have zero linear correlation. Does that prove tail independence?",[3844,3845,3847],"legacy-details",{"title":3846},"Answers",[2933,3848,3849,3852,3855],{},[2936,3850,3851],{},"£10m is the modelled 99th-percentile threshold, while £18m is the mean loss in the corresponding worst tail under the stated convention.",[2936,3853,3854],{},"It reduces Monte Carlo error conditional on the fitted model, not error from the wrong tail family, parameters, or dependence structure.",[2936,3856,3857],{},"No. Non-linear or tail dependence can remain even when covariance is zero.",[1844,3859,3861],{"id":3860},"sources-and-further-reading","Sources and further reading",[3317,3863,3864,3872,3881,3888],{},[2936,3865,3866,3867,3871],{},"Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D. (1999), “Coherent Measures of Risk,” ",[3868,3869,3870],"em",{},"Mathematical Finance",", 9(3), 203–228.",[2936,3873,3874],{},[3875,3876,3880],"a",{"href":3877,"rel":3878},"https:\u002F\u002Fwww.bankofengland.co.uk\u002Fprudential-regulation\u002Fpublication\u002F2015\u002Fsolvency2-the-solvency-and-minimum-capital-requirements-ss",[3879],"nofollow","Bank of England — Solvency II\u002FUK capital requirement supervisory statement",[2936,3882,3883],{},[3875,3884,3887],{"href":3885,"rel":3886},"https:\u002F\u002Fwww.bankofengland.co.uk\u002Fprudential-regulation\u002Fregulatory-reporting\u002Fregulatory-reporting-insurance-sector",[3879],"Bank of England — Solvency UK insurance reporting",[2936,3889,3890],{},[3875,3891,3894],{"href":3892,"rel":3893},"https:\u002F\u002Fwww.swissre.com\u002Fpress-release\u002FWildfires-storms-floods-contribute-to-record-92-of-global-insured-losses-in-2025-says-Swiss-Re-Institute\u002F7b39b1a5-b878-4a55-a5ff-bf5aa561a675",[3879],"Swiss Re Institute — natural catastrophes in 2025",[1793,3896,3897,3898,1966],{},"Next, move from a one-period loss distribution to ",[3875,3899,3901],{"href":3900},"..\u002F06-ruin-theory\u002F","surplus paths and ruin",{"title":10,"searchDepth":3903,"depth":3903,"links":3904},2,[3905,3906,3907,3908,3909,3910,3911,3912,3913],{"id":1846,"depth":3903,"text":1847},{"id":2778,"depth":3903,"text":2779},{"id":3020,"depth":3903,"text":3021},{"id":3037,"depth":3903,"text":3038},{"id":3339,"depth":3903,"text":3340},{"id":3598,"depth":3903,"text":3599},{"id":3608,"depth":3903,"text":3609},{"id":3629,"depth":3903,"text":3630},{"id":3860,"depth":3903,"text":3861},"Calculate VaR and TVaR, model common shocks, and preserve the boundary between risk theory and regulation.","md",{"sidebar":3917},{"order":3918},4,true,{"title":924,"description":3914},"7-o1S7XIxp45nr3leJrB7PtC55fPb2-Gehh5dyrvYCs",[3923,3925],{"title":920,"path":921,"stem":922,"description":3924,"children":-1},"Reconcile analytical moments with transparent R and Python simulations.",{"title":928,"path":929,"stem":930,"description":3926,"children":-1},"Analyse when a classical insurer surplus process crosses zero and preserve the model's practical boundaries.",1785754736918]