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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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This course develops one connected answer to five questions:",[1797,1798,1799,1807,1813,1819,1825],"ol",{},[1800,1801,1802,1806],"li",{},[1803,1804,1805],"strong",{},"Reserve:"," how much do claims that have already happened still cost?",[1800,1808,1809,1812],{},[1803,1810,1811],{},"Model:"," how often will claims occur, and how large can they be?",[1800,1814,1815,1818],{},[1803,1816,1817],{},"Transfer:"," which losses remain after reinsurance?",[1800,1820,1821,1824],{},[1803,1822,1823],{},"Aggregate:"," what can the whole portfolio lose in one period?",[1800,1826,1827,1830],{},[1803,1828,1829],{},"Survive:"," how much capital is needed against adverse paths through time?",[1793,1832,1833],{},"The pages are concise by design. Each new idea is introduced through a calculation, followed by the assumption that makes the calculation defensible.",[1835,1836,1838,1839,1842,1843,1842,1846,1842,1849,1852,1853,1856],"tip",{"title":1837},"The discipline of the course","Before choosing a formula, write down the ",[1803,1840,1841],{},"unit",", ",[1803,1844,1845],{},"time period",[1803,1847,1848],{},"information date",[1803,1850,1851],{},"loss basis",", and ",[1803,1854,1855],{},"decision",". Most serious insurance-model errors begin before any arithmetic is done.",[1858,1859,1861],"h2",{"id":1860},"learning-outcomes","Learning outcomes",[1793,1863,1864],{},"By the end, you should be able to:",[1866,1867,1868,1871,1874,1877,1880,1883,1886],"ul",{},[1800,1869,1870],{},"validate paid, incurred, and claim-count data before constructing a run-off triangle;",[1800,1872,1873],{},"calculate and critique chain-ladder, frequency–severity, and Bornhuetter–Ferguson reserves;",[1800,1875,1876],{},"choose frequency and severity models using exposure, tail, censoring, and validation evidence;",[1800,1878,1879],{},"translate proportional and excess-of-loss wording into retained-loss functions;",[1800,1881,1882],{},"derive or simulate aggregate-loss moments and tail measures;",[1800,1884,1885],{},"interpret classical ruin results without confusing them with accounting or regulatory capital;",[1800,1887,1888],{},"present a recommendation with assumptions, diagnostics, uncertainty, and limitations.",[1793,1890,1891],{},"These outcomes suit an upper-undergraduate course and provide a bridge to postgraduate stochastic reserving, extreme-value theory, credibility, and solvency modelling.",[1858,1893,1895],{"id":1894},"one-portfolio-used-throughout","One portfolio, used throughout",[1793,1897,1898,1901],{},[1803,1899,1900],{},"Harbour Mutual"," is a fictional UK motor insurer. All figures are synthetic unless a page explicitly labels an external data source.",[1903,1904,1905,1918],"table",{},[1906,1907,1908],"thead",{},[1909,1910,1911,1915],"tr",{},[1912,1913,1914],"th",{},"Item",[1912,1916,1917],{},"Course convention",[1919,1920,1921,1930,1938,1946,1954,1962,1970,1978],"tbody",{},[1909,1922,1923,1927],{},[1924,1925,1926],"td",{},"Valuation date",[1924,1928,1929],{},"31 December 2023",[1909,1931,1932,1935],{},[1924,1933,1934],{},"Origin period",[1924,1936,1937],{},"Accident year (AY)",[1909,1939,1940,1943],{},[1924,1941,1942],{},"Development age",[1924,1944,1945],{},"Years since the start of the accident year",[1909,1947,1948,1951],{},[1924,1949,1950],{},"Main triangle",[1924,1952,1953],{},"Cumulative paid own-damage loss, £m",[1909,1955,1956,1959],{},[1924,1957,1958],{},"Exposure",[1924,1960,1961],{},"Earned vehicle-years",[1909,1963,1964,1967],{},[1924,1965,1966],{},"Severity",[1924,1968,1969],{},"Ultimate cost per claim",[1909,1971,1972,1975],{},[1924,1973,1974],{},"Reinsurance",[1924,1976,1977],{},"Applied to each loss unless stated otherwise",[1909,1979,1980,1983],{},[1924,1981,1982],{},"Capital horizon",[1924,1984,1985],{},"One year for VaR\u002FTVaR; multiple years for ruin",[1793,1987,1988],{},"Its paid triangle is:",[1903,1990,1991,2011],{},[1906,1992,1993],{},[1909,1994,1995,1998,2002,2005,2008],{},[1912,1996,1997],{},"AY",[1912,1999,2001],{"align":2000},"right","Dev 0",[1912,2003,2004],{"align":2000},"Dev 1",[1912,2006,2007],{"align":2000},"Dev 2",[1912,2009,2010],{"align":2000},"Dev 3",[1919,2012,2013,2030,2047,2062],{},[1909,2014,2015,2018,2021,2024,2027],{},[1924,2016,2017],{},"2020",[1924,2019,2020],{"align":2000},"100",[1924,2022,2023],{"align":2000},"180",[1924,2025,2026],{"align":2000},"240",[1924,2028,2029],{"align":2000},"280",[1909,2031,2032,2035,2038,2041,2044],{},[1924,2033,2034],{},"2021",[1924,2036,2037],{"align":2000},"120",[1924,2039,2040],{"align":2000},"220",[1924,2042,2043],{"align":2000},"300",[1924,2045,2046],{"align":2000},"—",[1909,2048,2049,2052,2055,2058,2060],{},[1924,2050,2051],{},"2022",[1924,2053,2054],{"align":2000},"140",[1924,2056,2057],{"align":2000},"260",[1924,2059,2046],{"align":2000},[1924,2061,2046],{"align":2000},[1909,2063,2064,2067,2070,2072,2074],{},[1924,2065,2066],{},"2023",[1924,2068,2069],{"align":2000},"160",[1924,2071,2046],{"align":2000},[1924,2073,2046],{"align":2000},[1924,2075,2046],{"align":2000},[1793,2077,2078,2079,2082],{},"Blank cells are ",[1803,2080,2081],{},"unobserved future development",", not zero. With volume-weighted age-to-age factors,",[2084,2085,2088],"span",{"className":2086},[2087],"katex-display",[2084,2089,2092,2215],{"className":2090},[2091],"katex",[2084,2093,2096],{"className":2094},[2095],"katex-mathml",[2097,2098,2101],"math",{"xmlns":2099,"display":2100},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[2102,2103,2104,2210],"semantics",{},[2105,2106,2107,2127,2130,2139,2141,2144,2148,2152,2165,2167,2175,2177,2180,2182,2184,2197,2199,2205,2207],"mrow",{},[2108,2109,2110,2114],"msub",{},[2111,2112,2113],"mi",{},"f",[2105,2115,2116,2120,2124],{},[2117,2118,2119],"mn",{},"0",[2121,2122,2123],"mo",{},":",[2117,2125,2126],{},"1",[2121,2128,2129],{},"=",[2131,2132,2133,2136],"mfrac",{},[2117,2134,2135],{},"660",[2117,2137,2138],{},"360",[2121,2140,2129],{},[2117,2142,2143],{},"1.8333",[2121,2145,2147],{"separator":2146},"true",",",[2149,2150],"mspace",{"width":2151},"2em",[2108,2153,2154,2156],{},[2111,2155,2113],{},[2105,2157,2158,2160,2162],{},[2117,2159,2126],{},[2121,2161,2123],{},[2117,2163,2164],{},"2",[2121,2166,2129],{},[2131,2168,2169,2172],{},[2117,2170,2171],{},"540",[2117,2173,2174],{},"400",[2121,2176,2129],{},[2117,2178,2179],{},"1.35",[2121,2181,2147],{"separator":2146},[2149,2183],{"width":2151},[2108,2185,2186,2188],{},[2111,2187,2113],{},[2105,2189,2190,2192,2194],{},[2117,2191,2164],{},[2121,2193,2123],{},[2117,2195,2196],{},"3",[2121,2198,2129],{},[2131,2200,2201,2203],{},[2117,2202,2029],{},[2117,2204,2026],{},[2121,2206,2129],{},[2117,2208,2209],{},"1.1667.",[2211,2212,2214],"annotation",{"encoding":2213},"application\u002Fx-tex","f_{0:1}=\\frac{660}{360}=1.8333,\\qquad\nf_{1:2}=\\frac{540}{400}=1.35,\\qquad\nf_{2:3}=\\frac{280}{240}=1.1667.",[2084,2216,2219,2307,2396,2475,2552,2628,2705],{"className":2217,"ariaHidden":2146},[2218],"katex-html",[2084,2220,2223,2228,2297,2301,2304],{"className":2221},[2222],"base",[2084,2224],{"className":2225,"style":2227},[2226],"strut","height:0.8889em;vertical-align:-0.1944em;",[2084,2229,2232,2237],{"className":2230},[2231],"mord",[2084,2233,2113],{"className":2234,"style":2236},[2231,2235],"mathnormal","margin-right:0.1076em;",[2084,2238,2241],{"className":2239},[2240],"msupsub",[2084,2242,2246,2288],{"className":2243},[2244,2245],"vlist-t","vlist-t2",[2084,2247,2250,2283],{"className":2248},[2249],"vlist-r",[2084,2251,2255],{"className":2252,"style":2254},[2253],"vlist","height:0.3011em;",[2084,2256,2258,2263],{"style":2257},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[2084,2259],{"className":2260,"style":2262},[2261],"pstrut","height:2.7em;",[2084,2264,2270],{"className":2265},[2266,2267,2268,2269],"sizing","reset-size6","size3","mtight",[2084,2271,2273,2276,2280],{"className":2272},[2231,2269],[2084,2274,2119],{"className":2275},[2231,2269],[2084,2277,2123],{"className":2278},[2279,2269],"mrel",[2084,2281,2126],{"className":2282},[2231,2269],[2084,2284,2287],{"className":2285},[2286],"vlist-s","​",[2084,2289,2291],{"className":2290},[2249],[2084,2292,2295],{"className":2293,"style":2294},[2253],"height:0.15em;",[2084,2296],{},[2084,2298],{"className":2299,"style":2300},[2149],"margin-right:0.2778em;",[2084,2302,2129],{"className":2303},[2279],[2084,2305],{"className":2306,"style":2300},[2149],[2084,2308,2310,2314,2387,2390,2393],{"className":2309},[2222],[2084,2311],{"className":2312,"style":2313},[2226],"height:2.0074em;vertical-align:-0.686em;",[2084,2315,2317,2322,2383],{"className":2316},[2231],[2084,2318],{"className":2319},[2320,2321],"mopen","nulldelimiter",[2084,2323,2325],{"className":2324},[2131],[2084,2326,2328,2374],{"className":2327},[2244,2245],[2084,2329,2331,2371],{"className":2330},[2249],[2084,2332,2335,2348,2359],{"className":2333,"style":2334},[2253],"height:1.3214em;",[2084,2336,2338,2342],{"style":2337},"top:-2.314em;",[2084,2339],{"className":2340,"style":2341},[2261],"height:3em;",[2084,2343,2345],{"className":2344},[2231],[2084,2346,2138],{"className":2347},[2231],[2084,2349,2351,2354],{"style":2350},"top:-3.23em;",[2084,2352],{"className":2353,"style":2341},[2261],[2084,2355],{"className":2356,"style":2358},[2357],"frac-line","border-bottom-width:0.04em;",[2084,2360,2362,2365],{"style":2361},"top:-3.677em;",[2084,2363],{"className":2364,"style":2341},[2261],[2084,2366,2368],{"className":2367},[2231],[2084,2369,2135],{"className":2370},[2231],[2084,2372,2287],{"className":2373},[2286],[2084,2375,2377],{"className":2376},[2249],[2084,2378,2381],{"className":2379,"style":2380},[2253],"height:0.686em;",[2084,2382],{},[2084,2384],{"className":2385},[2386,2321],"mclose",[2084,2388],{"className":2389,"style":2300},[2149],[2084,2391,2129],{"className":2392},[2279],[2084,2394],{"className":2395,"style":2300},[2149],[2084,2397,2399,2402,2405,2409,2413,2417,2466,2469,2472],{"className":2398},[2222],[2084,2400],{"className":2401,"style":2227},[2226],[2084,2403,2143],{"className":2404},[2231],[2084,2406,2147],{"className":2407},[2408],"mpunct",[2084,2410],{"className":2411,"style":2412},[2149],"margin-right:2em;",[2084,2414],{"className":2415,"style":2416},[2149],"margin-right:0.1667em;",[2084,2418,2420,2423],{"className":2419},[2231],[2084,2421,2113],{"className":2422,"style":2236},[2231,2235],[2084,2424,2426],{"className":2425},[2240],[2084,2427,2429,2458],{"className":2428},[2244,2245],[2084,2430,2432,2455],{"className":2431},[2249],[2084,2433,2435],{"className":2434,"style":2254},[2253],[2084,2436,2437,2440],{"style":2257},[2084,2438],{"className":2439,"style":2262},[2261],[2084,2441,2443],{"className":2442},[2266,2267,2268,2269],[2084,2444,2446,2449,2452],{"className":2445},[2231,2269],[2084,2447,2126],{"className":2448},[2231,2269],[2084,2450,2123],{"className":2451},[2279,2269],[2084,2453,2164],{"className":2454},[2231,2269],[2084,2456,2287],{"className":2457},[2286],[2084,2459,2461],{"className":2460},[2249],[2084,2462,2464],{"className":2463,"style":2294},[2253],[2084,2465],{},[2084,2467],{"className":2468,"style":2300},[2149],[2084,2470,2129],{"className":2471},[2279],[2084,2473],{"className":2474,"style":2300},[2149],[2084,2476,2478,2481,2543,2546,2549],{"className":2477},[2222],[2084,2479],{"className":2480,"style":2313},[2226],[2084,2482,2484,2487,2540],{"className":2483},[2231],[2084,2485],{"className":2486},[2320,2321],[2084,2488,2490],{"className":2489},[2131],[2084,2491,2493,2532],{"className":2492},[2244,2245],[2084,2494,2496,2529],{"className":2495},[2249],[2084,2497,2499,2510,2518],{"className":2498,"style":2334},[2253],[2084,2500,2501,2504],{"style":2337},[2084,2502],{"className":2503,"style":2341},[2261],[2084,2505,2507],{"className":2506},[2231],[2084,2508,2174],{"className":2509},[2231],[2084,2511,2512,2515],{"style":2350},[2084,2513],{"className":2514,"style":2341},[2261],[2084,2516],{"className":2517,"style":2358},[2357],[2084,2519,2520,2523],{"style":2361},[2084,2521],{"className":2522,"style":2341},[2261],[2084,2524,2526],{"className":2525},[2231],[2084,2527,2171],{"className":2528},[2231],[2084,2530,2287],{"className":2531},[2286],[2084,2533,2535],{"className":2534},[2249],[2084,2536,2538],{"className":2537,"style":2380},[2253],[2084,2539],{},[2084,2541],{"className":2542},[2386,2321],[2084,2544],{"className":2545,"style":2300},[2149],[2084,2547,2129],{"className":2548},[2279],[2084,2550],{"className":2551,"style":2300},[2149],[2084,2553,2555,2558,2561,2564,2567,2570,2619,2622,2625],{"className":2554},[2222],[2084,2556],{"className":2557,"style":2227},[2226],[2084,2559,2179],{"className":2560},[2231],[2084,2562,2147],{"className":2563},[2408],[2084,2565],{"className":2566,"style":2412},[2149],[2084,2568],{"className":2569,"style":2416},[2149],[2084,2571,2573,2576],{"className":2572},[2231],[2084,2574,2113],{"className":2575,"style":2236},[2231,2235],[2084,2577,2579],{"className":2578},[2240],[2084,2580,2582,2611],{"className":2581},[2244,2245],[2084,2583,2585,2608],{"className":2584},[2249],[2084,2586,2588],{"className":2587,"style":2254},[2253],[2084,2589,2590,2593],{"style":2257},[2084,2591],{"className":2592,"style":2262},[2261],[2084,2594,2596],{"className":2595},[2266,2267,2268,2269],[2084,2597,2599,2602,2605],{"className":2598},[2231,2269],[2084,2600,2164],{"className":2601},[2231,2269],[2084,2603,2123],{"className":2604},[2279,2269],[2084,2606,2196],{"className":2607},[2231,2269],[2084,2609,2287],{"className":2610},[2286],[2084,2612,2614],{"className":2613},[2249],[2084,2615,2617],{"className":2616,"style":2294},[2253],[2084,2618],{},[2084,2620],{"className":2621,"style":2300},[2149],[2084,2623,2129],{"className":2624},[2279],[2084,2626],{"className":2627,"style":2300},[2149],[2084,2629,2631,2634,2696,2699,2702],{"className":2630},[2222],[2084,2632],{"className":2633,"style":2313},[2226],[2084,2635,2637,2640,2693],{"className":2636},[2231],[2084,2638],{"className":2639},[2320,2321],[2084,2641,2643],{"className":2642},[2131],[2084,2644,2646,2685],{"className":2645},[2244,2245],[2084,2647,2649,2682],{"className":2648},[2249],[2084,2650,2652,2663,2671],{"className":2651,"style":2334},[2253],[2084,2653,2654,2657],{"style":2337},[2084,2655],{"className":2656,"style":2341},[2261],[2084,2658,2660],{"className":2659},[2231],[2084,2661,2026],{"className":2662},[2231],[2084,2664,2665,2668],{"style":2350},[2084,2666],{"className":2667,"style":2341},[2261],[2084,2669],{"className":2670,"style":2358},[2357],[2084,2672,2673,2676],{"style":2361},[2084,2674],{"className":2675,"style":2341},[2261],[2084,2677,2679],{"className":2678},[2231],[2084,2680,2029],{"className":2681},[2231],[2084,2683,2287],{"className":2684},[2286],[2084,2686,2688],{"className":2687},[2249],[2084,2689,2691],{"className":2690,"style":2380},[2253],[2084,2692],{},[2084,2694],{"className":2695},[2386,2321],[2084,2697],{"className":2698,"style":2300},[2149],[2084,2700,2129],{"className":2701},[2279],[2084,2703],{"className":2704,"style":2300},[2149],[2084,2706,2708,2712],{"className":2707},[2222],[2084,2709],{"className":2710,"style":2711},[2226],"height:0.6444em;",[2084,2713,2209],{"className":2714},[2231],[1793,2716,2717],{},"This gives the following baseline—not a final professional opinion:",[1903,2719,2720,2735],{},[1906,2721,2722],{},[1909,2723,2724,2726,2729,2732],{},[1912,2725,1997],{},[1912,2727,2728],{"align":2000},"Latest paid",[1912,2730,2731],{"align":2000},"Projected ultimate",[1912,2733,2734],{"align":2000},"Reserve",[1919,2736,2737,2749,2762,2775,2788],{},[1909,2738,2739,2741,2744,2746],{},[1924,2740,2017],{},[1924,2742,2743],{"align":2000},"280.0",[1924,2745,2743],{"align":2000},[1924,2747,2748],{"align":2000},"0.0",[1909,2750,2751,2753,2756,2759],{},[1924,2752,2034],{},[1924,2754,2755],{"align":2000},"300.0",[1924,2757,2758],{"align":2000},"350.0",[1924,2760,2761],{"align":2000},"50.0",[1909,2763,2764,2766,2769,2772],{},[1924,2765,2051],{},[1924,2767,2768],{"align":2000},"260.0",[1924,2770,2771],{"align":2000},"409.5",[1924,2773,2774],{"align":2000},"149.5",[1909,2776,2777,2779,2782,2785],{},[1924,2778,2066],{},[1924,2780,2781],{"align":2000},"160.0",[1924,2783,2784],{"align":2000},"462.0",[1924,2786,2787],{"align":2000},"302.0",[1909,2789,2790,2795,2800,2805],{},[1924,2791,2792],{},[1803,2793,2794],{},"Total",[1924,2796,2797],{"align":2000},[1803,2798,2799],{},"1,000.0",[1924,2801,2802],{"align":2000},[1803,2803,2804],{},"1,501.5",[1924,2806,2807],{"align":2000},[1803,2808,2809],{},"501.5",[1793,2811,2812,2813,2818],{},"The calculation is easy. The hard question is whether past development is stable enough to project the unobserved cells. The ",[2814,2815,2817],"a",{"href":2816},"..\u002F02-chain-ladder\u002F","reserving module"," makes that question explicit.",[1858,2820,2822],{"id":2821},"vocabulary-that-changes-the-model","Vocabulary that changes the model",[1903,2824,2825,2838],{},[1906,2826,2827],{},[1909,2828,2829,2832,2835],{},[1912,2830,2831],{},"Term",[1912,2833,2834],{},"Operational meaning",[1912,2836,2837],{},"Common mistake",[1919,2839,2840,2851,2862,2873,2884,2895,2905,2916],{},[1909,2841,2842,2845,2848],{},[1924,2843,2844],{},"Paid loss",[1924,2846,2847],{},"Cash paid by the valuation date",[1924,2849,2850],{},"Treating settlement speed as claim severity",[1909,2852,2853,2856,2859],{},[1924,2854,2855],{},"Case reserve",[1924,2857,2858],{},"Current estimate on a reported, unsettled claim",[1924,2860,2861],{},"Assuming adjuster practice is stable",[1909,2863,2864,2867,2870],{},[1924,2865,2866],{},"Incurred loss",[1924,2868,2869],{},"Usually paid plus case reserve",[1924,2871,2872],{},"Using the label without documenting the organisation's definition",[1909,2874,2875,2878,2881],{},[1924,2876,2877],{},"IBNR",[1924,2879,2880],{},"Future recognition of losses already incurred; usage may include development on known claims",[1924,2882,2883],{},"Treating every organisation's IBNR convention as identical",[1909,2885,2886,2889,2892],{},[1924,2887,2888],{},"Ultimate loss",[1924,2890,2891],{},"Expected cost after all development",[1924,2893,2894],{},"Calling the oldest observed cell “ultimate” without evidence",[1909,2896,2897,2899,2902],{},[1924,2898,1958],{},[1924,2900,2901],{},"Amount of insured risk, such as vehicle-years",[1924,2903,2904],{},"Comparing raw counts when portfolio size changed",[1909,2906,2907,2910,2913],{},[1924,2908,2909],{},"Deductible",[1924,2911,2912],{},"Amount borne by the policyholder",[1924,2914,2915],{},"Fitting the observed payment distribution as if it were ground-up loss",[1909,2917,2918,2921,2924],{},[1924,2919,2920],{},"Policy\u002Freinsurance limit",[1924,2922,2923],{},"Maximum payment under stated terms",[1924,2925,2926],{},"Using an unlimited severity model without applying the contract",[1793,2928,2929],{},"Two identities organise the course:",[2084,2931,2933],{"className":2932},[2087],[2084,2934,2936,2971],{"className":2935},[2091],[2084,2937,2939],{"className":2938},[2095],[2097,2940,2941],{"xmlns":2099,"display":2100},[2102,2942,2943,2968],{},[2105,2944,2945,2949,2951,2960,2963,2966],{},[2946,2947,2948],"mtext",{},"reserve",[2121,2950,2129],{},[2952,2953,2954,2957],"mover",{"accent":2146},[2946,2955,2956],{},"ultimate loss",[2121,2958,2959],{"stretchy":2146},"^",[2121,2961,2962],{},"−",[2946,2964,2965],{},"loss observed to date",[2121,2967,2147],{"separator":2146},[2211,2969,2970],{"encoding":2213},"\\text{reserve}=\\widehat{\\text{ultimate loss}}-\\text{loss observed to date},",[2084,2972,2974,2997,3064],{"className":2973,"ariaHidden":2146},[2218],[2084,2975,2977,2981,2988,2991,2994],{"className":2976},[2222],[2084,2978],{"className":2979,"style":2980},[2226],"height:0.4306em;",[2084,2982,2985],{"className":2983},[2231,2984],"text",[2084,2986,2948],{"className":2987},[2231],[2084,2989],{"className":2990,"style":2300},[2149],[2084,2992,2129],{"className":2993},[2279],[2084,2995],{"className":2996,"style":2300},[2149],[2084,2998,3000,3004,3053,3057,3061],{"className":2999},[2222],[2084,3001],{"className":3002,"style":3003},[2226],"height:1.0178em;vertical-align:-0.0833em;",[2084,3005,3008],{"className":3006},[2231,3007],"accent",[2084,3009,3011],{"className":3010},[2244],[2084,3012,3014],{"className":3013},[2249],[2084,3015,3018,3030],{"className":3016,"style":3017},[2253],"height:0.9344em;",[2084,3019,3021,3024],{"style":3020},"top:-3em;",[2084,3022],{"className":3023,"style":2341},[2261],[2084,3025,3027],{"className":3026},[2231,2984],[2084,3028,2956],{"className":3029},[2231],[2084,3031,3035,3038],{"className":3032,"style":3034},[3033],"svg-align","top:-3.6944em;",[2084,3036],{"className":3037,"style":2341},[2261],[2084,3039,3041],{"style":3040},"height:0.24em;",[3042,3043,3049],"svg",{"xmlns":3044,"width":3045,"height":3046,"viewBox":3047,"preserveAspectRatio":3048},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","100%","0.24em","0 0 1062 239","none",[3050,3051],"path",{"d":3052},"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",[2084,3054],{"className":3055,"style":3056},[2149],"margin-right:0.2222em;",[2084,3058,2962],{"className":3059},[3060],"mbin",[2084,3062],{"className":3063,"style":3056},[2149],[2084,3065,3067,3070,3076],{"className":3066},[2222],[2084,3068],{"className":3069,"style":2227},[2226],[2084,3071,3073],{"className":3072},[2231,2984],[2084,3074,2965],{"className":3075},[2231],[2084,3077,2147],{"className":3078},[2408],[2084,3080,3082],{"className":3081},[2087],[2084,3083,3085,3129],{"className":3084},[2091],[2084,3086,3088],{"className":3087},[2095],[2097,3089,3090],{"xmlns":2099,"display":2100},[2102,3091,3092,3126],{},[2105,3093,3094,3097,3099,3117,3124],{},[2111,3095,3096],{},"S",[2121,3098,2129],{},[3100,3101,3102,3105,3114],"munderover",{},[2121,3103,3104],{},"∑",[2105,3106,3107,3110,3112],{},[2111,3108,3109],{},"i",[2121,3111,2129],{},[2117,3113,2126],{},[2111,3115,3116],{},"N",[2108,3118,3119,3122],{},[2111,3120,3121],{},"X",[2111,3123,3109],{},[2121,3125,2147],{"separator":2146},[2211,3127,3128],{"encoding":2213},"S=\\sum_{i=1}^{N}X_i,",[2084,3130,3132,3152],{"className":3131,"ariaHidden":2146},[2218],[2084,3133,3135,3139,3143,3146,3149],{"className":3134},[2222],[2084,3136],{"className":3137,"style":3138},[2226],"height:0.6833em;",[2084,3140,3096],{"className":3141,"style":3142},[2231,2235],"margin-right:0.0576em;",[2084,3144],{"className":3145,"style":2300},[2149],[2084,3147,2129],{"className":3148},[2279],[2084,3150],{"className":3151,"style":2300},[2149],[2084,3153,3155,3159,3237,3240,3283],{"className":3154},[2222],[2084,3156],{"className":3157,"style":3158},[2226],"height:3.106em;vertical-align:-1.2777em;",[2084,3160,3164],{"className":3161},[3162,3163],"mop","op-limits",[2084,3165,3167,3228],{"className":3166},[2244,2245],[2084,3168,3170,3225],{"className":3169},[2249],[2084,3171,3174,3196,3209],{"className":3172,"style":3173},[2253],"height:1.8283em;",[2084,3175,3177,3181],{"style":3176},"top:-1.8723em;margin-left:0em;",[2084,3178],{"className":3179,"style":3180},[2261],"height:3.05em;",[2084,3182,3184],{"className":3183},[2266,2267,2268,2269],[2084,3185,3187,3190,3193],{"className":3186},[2231,2269],[2084,3188,3109],{"className":3189},[2231,2235,2269],[2084,3191,2129],{"className":3192},[2279,2269],[2084,3194,2126],{"className":3195},[2231,2269],[2084,3197,3199,3202],{"style":3198},"top:-3.05em;",[2084,3200],{"className":3201,"style":3180},[2261],[2084,3203,3204],{},[2084,3205,3104],{"className":3206},[3162,3207,3208],"op-symbol","large-op",[2084,3210,3212,3215],{"style":3211},"top:-4.3em;margin-left:0em;",[2084,3213],{"className":3214,"style":3180},[2261],[2084,3216,3218],{"className":3217},[2266,2267,2268,2269],[2084,3219,3221],{"className":3220},[2231,2269],[2084,3222,3116],{"className":3223,"style":3224},[2231,2235,2269],"margin-right:0.109em;",[2084,3226,2287],{"className":3227},[2286],[2084,3229,3231],{"className":3230},[2249],[2084,3232,3235],{"className":3233,"style":3234},[2253],"height:1.2777em;",[2084,3236],{},[2084,3238],{"className":3239,"style":2416},[2149],[2084,3241,3243,3247],{"className":3242},[2231],[2084,3244,3121],{"className":3245,"style":3246},[2231,2235],"margin-right:0.0785em;",[2084,3248,3250],{"className":3249},[2240],[2084,3251,3253,3275],{"className":3252},[2244,2245],[2084,3254,3256,3272],{"className":3255},[2249],[2084,3257,3260],{"className":3258,"style":3259},[2253],"height:0.3117em;",[2084,3261,3263,3266],{"style":3262},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[2084,3264],{"className":3265,"style":2262},[2261],[2084,3267,3269],{"className":3268},[2266,2267,2268,2269],[2084,3270,3109],{"className":3271},[2231,2235,2269],[2084,3273,2287],{"className":3274},[2286],[2084,3276,3278],{"className":3277},[2249],[2084,3279,3281],{"className":3280,"style":2294},[2253],[2084,3282],{},[2084,3284,2147],{"className":3285},[2408],[1793,3287,3288,3289,3317,3318,3389,3390,3418],{},"where ",[2084,3290,3292,3305],{"className":3291},[2091],[2084,3293,3295],{"className":3294},[2095],[2097,3296,3297],{"xmlns":2099},[2102,3298,3299,3303],{},[2105,3300,3301],{},[2111,3302,3116],{},[2211,3304,3116],{"encoding":2213},[2084,3306,3308],{"className":3307,"ariaHidden":2146},[2218],[2084,3309,3311,3314],{"className":3310},[2222],[2084,3312],{"className":3313,"style":3138},[2226],[2084,3315,3116],{"className":3316,"style":3224},[2231,2235]," is claim frequency, ",[2084,3319,3321,3339],{"className":3320},[2091],[2084,3322,3324],{"className":3323},[2095],[2097,3325,3326],{"xmlns":2099},[2102,3327,3328,3336],{},[2105,3329,3330],{},[2108,3331,3332,3334],{},[2111,3333,3121],{},[2111,3335,3109],{},[2211,3337,3338],{"encoding":2213},"X_i",[2084,3340,3342],{"className":3341,"ariaHidden":2146},[2218],[2084,3343,3345,3349],{"className":3344},[2222],[2084,3346],{"className":3347,"style":3348},[2226],"height:0.8333em;vertical-align:-0.15em;",[2084,3350,3352,3355],{"className":3351},[2231],[2084,3353,3121],{"className":3354,"style":3246},[2231,2235],[2084,3356,3358],{"className":3357},[2240],[2084,3359,3361,3381],{"className":3360},[2244,2245],[2084,3362,3364,3378],{"className":3363},[2249],[2084,3365,3367],{"className":3366,"style":3259},[2253],[2084,3368,3369,3372],{"style":3262},[2084,3370],{"className":3371,"style":2262},[2261],[2084,3373,3375],{"className":3374},[2266,2267,2268,2269],[2084,3376,3109],{"className":3377},[2231,2235,2269],[2084,3379,2287],{"className":3380},[2286],[2084,3382,3384],{"className":3383},[2249],[2084,3385,3387],{"className":3386,"style":2294},[2253],[2084,3388],{}," is severity, and ",[2084,3391,3393,3406],{"className":3392},[2091],[2084,3394,3396],{"className":3395},[2095],[2097,3397,3398],{"xmlns":2099},[2102,3399,3400,3404],{},[2105,3401,3402],{},[2111,3403,3096],{},[2211,3405,3096],{"encoding":2213},[2084,3407,3409],{"className":3408,"ariaHidden":2146},[2218],[2084,3410,3412,3415],{"className":3411},[2222],[2084,3413],{"className":3414,"style":3138},[2226],[2084,3416,3096],{"className":3417,"style":3142},[2231,2235]," is aggregate loss. These identities do not specify a model; they tell us what must be estimated.",[1858,3420,3422],{"id":3421},"course-route","Course route",[3424,3425],"mermaid-diagram",{"code64":3426,"locale":7},"Zmxvd2NoYXJ0IExSCiAgRFsiRGF0YSBjb250cmFjdCJdIC0tPiBSWyJSZXNlcnZlIHBhc3QgZXZlbnRzIl0KICBEIC0tPiBGWyJNb2RlbCBjb3VudCBhbmQgc2V2ZXJpdHkiXQogIEYgLS0+IFhbIkFwcGx5IHJlaW5zdXJhbmNlIHRlcm1zIl0KICBSIC0tPiBBWyJBZ2dyZWdhdGUgcmV0YWluZWQgcmlzayJdCiAgWCAtLT4gQQogIEEgLS0+IENbIlRhaWwgY2FwaXRhbCJdCiAgQyAtLT4gVVsiU3VycGx1cyBhbmQgcnVpbiJdCiAgVSAtLT4gUFsiSW50ZWdyYXRlZCBwb3J0Zm9saW8gZGVjaXNpb24iXQ==",[1903,3428,3429,3445],{},[1906,3430,3431],{},[1909,3432,3433,3436,3439,3442],{},[1912,3434,3435],{},"Unit",[1912,3437,3438],{},"Preparation",[1912,3440,3441],{},"In-class question",[1912,3443,3444],{},"Evidence produced",[1919,3446,3447,3461,3475,3493,3507,3521,3535],{},[1909,3448,3449,3452,3455,3458],{},[1924,3450,3451],{},"1. Data and reserving",[1924,3453,3454],{},"cumulative vs incremental claims",[1924,3456,3457],{},"Which cells are observed, and as of when?",[1924,3459,3460],{},"validated triangle and data contract",[1909,3462,3463,3466,3469,3472],{},[1924,3464,3465],{},"2. Reserving methods",[1924,3467,3468],{},"weighted averages; expected loss ratio",[1924,3470,3471],{},"What makes a development pattern credible?",[1924,3473,3474],{},"chain-ladder, frequency–severity, and BF comparison",[1909,3476,3477,3480,3483,3490],{},[1924,3478,3479],{},"3. Severity",[1924,3481,3482],{},"survival functions and quantiles",[1924,3484,3485,3486,3489],{},"Which model fits the centre ",[1803,3487,3488],{},"and"," the tail?",[1924,3491,3492],{},"fitted models and out-of-sample diagnostics",[1909,3494,3495,3498,3501,3504],{},[1924,3496,3497],{},"4. Frequency",[1924,3499,3500],{},"Poisson and conditional expectation",[1924,3502,3503],{},"Is variance larger than the mean because exposure or risk differs?",[1924,3505,3506],{},"exposure-adjusted count model",[1909,3508,3509,3512,3515,3518],{},[1924,3510,3511],{},"5. Reinsurance",[1924,3513,3514],{},"functions and layer notation",[1924,3516,3517],{},"What exactly is retained for this claim or event?",[1924,3519,3520],{},"contract loss transformation",[1909,3522,3523,3526,3529,3532],{},[1924,3524,3525],{},"6. Aggregate risk",[1924,3527,3528],{},"expectation, variance, simulation",[1924,3530,3531],{},"How do count, severity, and dependence combine?",[1924,3533,3534],{},"simulated loss distribution and tail measures",[1909,3536,3537,3540,3543,3546],{},[1924,3538,3539],{},"7. Ruin and capstone",[1924,3541,3542],{},"surplus processes",[1924,3544,3545],{},"What does the model omit from a real capital decision?",[1924,3547,3548],{},"recommendation with limitations",[1793,3550,3551,3552,3555],{},"Suggested workload is ",[1803,3553,3554],{},"2 hours of preparation, 2 hours in class, and 2 hours of practice per unit",". Students who have not used simulation should add one hour to Units 3 and 6. Every executable example runs in the page; no local Python or R installation is required.",[1858,3557,3559],{"id":3558},"a-10-minute-readiness-check","A 10-minute readiness check",[1797,3561,3562,3565,3568,3571,3574],{},[1800,3563,3564],{},"A portfolio has 25,000 vehicle-years and 1,000 claims. What is observed frequency per vehicle-year?",[1800,3566,3567],{},"Expected claim count is 100 and expected severity is £2,000. Is aggregate loss always £200,000?",[1800,3569,3570],{},"A £120,000 claim enters an unlimited £50,000 excess-of-loss layer. What is retained?",[1800,3572,3573],{},"Why can paid and incurred triangles produce different reserves?",[1800,3575,3576],{},"Why is a 99.5% one-year VaR not the same object as an ultimate ruin probability?",[3578,3579,3581],"legacy-details",{"title":3580},"Answers",[1797,3582,3583,3667,3776,3779,3782],{},[1800,3584,3585,3666],{},[2084,3586,3588,3615],{"className":3587},[2091],[2084,3589,3591],{"className":3590},[2095],[2097,3592,3593],{"xmlns":2099},[2102,3594,3595,3612],{},[2105,3596,3597,3600,3604,3607,3609],{},[2117,3598,3599],{},"1,000",[2111,3601,3603],{"mathvariant":3602},"normal","\u002F",[2117,3605,3606],{},"25,000",[2121,3608,2129],{},[2117,3610,3611],{},"0.04",[2211,3613,3614],{"encoding":2213},"1{,}000\u002F25{,}000=0.04",[2084,3616,3618,3657],{"className":3617,"ariaHidden":2146},[2218],[2084,3619,3621,3625,3628,3634,3638,3644,3648,3651,3654],{"className":3620},[2222],[2084,3622],{"className":3623,"style":3624},[2226],"height:1em;vertical-align:-0.25em;",[2084,3626,2126],{"className":3627},[2231],[2084,3629,3631],{"className":3630},[2231],[2084,3632,2147],{"className":3633},[2408],[2084,3635,3637],{"className":3636},[2231],"000\u002F25",[2084,3639,3641],{"className":3640},[2231],[2084,3642,2147],{"className":3643},[2408],[2084,3645,3647],{"className":3646},[2231],"000",[2084,3649],{"className":3650,"style":2300},[2149],[2084,3652,2129],{"className":3653},[2279],[2084,3655],{"className":3656,"style":2300},[2149],[2084,3658,3660,3663],{"className":3659},[2222],[2084,3661],{"className":3662,"style":2711},[2226],[2084,3664,3611],{"className":3665},[2231]," claims per vehicle-year.",[1800,3668,3669,3670,3775],{},"No. Under standard independence assumptions £200,000 is ",[2084,3671,3673,3715],{"className":3672},[2091],[2084,3674,3676],{"className":3675},[2095],[2097,3677,3678],{"xmlns":2099},[2102,3679,3680,3712],{},[2105,3681,3682,3685,3689,3691,3694,3696,3698,3700,3702,3704,3706,3708,3710],{},[2111,3683,3684],{},"E",[2121,3686,3688],{"stretchy":3687},"false","[",[2111,3690,3096],{},[2121,3692,3693],{"stretchy":3687},"]",[2121,3695,2129],{},[2111,3697,3684],{},[2121,3699,3688],{"stretchy":3687},[2111,3701,3116],{},[2121,3703,3693],{"stretchy":3687},[2111,3705,3684],{},[2121,3707,3688],{"stretchy":3687},[2111,3709,3121],{},[2121,3711,3693],{"stretchy":3687},[2211,3713,3714],{"encoding":2213},"E[S]=E[N]E[X]",[2084,3716,3718,3745],{"className":3717,"ariaHidden":2146},[2218],[2084,3719,3721,3724,3727,3730,3733,3736,3739,3742],{"className":3720},[2222],[2084,3722],{"className":3723,"style":3624},[2226],[2084,3725,3684],{"className":3726,"style":3142},[2231,2235],[2084,3728,3688],{"className":3729},[2320],[2084,3731,3096],{"className":3732,"style":3142},[2231,2235],[2084,3734,3693],{"className":3735},[2386],[2084,3737],{"className":3738,"style":2300},[2149],[2084,3740,2129],{"className":3741},[2279],[2084,3743],{"className":3744,"style":2300},[2149],[2084,3746,3748,3751,3754,3757,3760,3763,3766,3769,3772],{"className":3747},[2222],[2084,3749],{"className":3750,"style":3624},[2226],[2084,3752,3684],{"className":3753,"style":3142},[2231,2235],[2084,3755,3688],{"className":3756},[2320],[2084,3758,3116],{"className":3759,"style":3224},[2231,2235],[2084,3761,3693],{"className":3762},[2386],[2084,3764,3684],{"className":3765,"style":3142},[2231,2235],[2084,3767,3688],{"className":3768},[2320],[2084,3770,3121],{"className":3771,"style":3246},[2231,2235],[2084,3773,3693],{"className":3774},[2386],", not the realised loss.",[1800,3777,3778],{},"The insurer retains £50,000 and cedes £70,000.",[1800,3780,3781],{},"Paid data reflect settlement timing; incurred data also reflect case-reserving practice. Either process may change.",[1800,3783,3784],{},"They use different horizons, loss definitions, and dynamics. VaR is a quantile of a specified one-year distribution; ruin is a path event in a surplus process.",[1858,3786,3788],{"id":3787},"first-executable-example-from-claims-to-retained-loss","First executable example: from claims to retained loss",[1793,3790,3791],{},"Suppose annual count is Poisson with mean 40 and individual loss is lognormal with mean about £5,000. Compare gross loss with a £20,000 per-loss retention. Change the seed or retention and rerun.",[3793,3794],"pyodide",{"code64":3795,"layout":3796,"locale":7,"packages":3797,"title":3798},"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","vertical","numpy,matplotlib","Gross and retained annual loss",[1793,3800,3801],{},"The example previews three important points: an expected value does not describe tail risk; reinsurance acts on a precisely defined loss; and simulation answers only the model we programmed.",[1858,3803,3805],{"id":3804},"contemporary-contextand-its-boundary","Contemporary context—and its boundary",[1866,3807,3808,3814,3820],{},[1800,3809,3810,3813],{},[1803,3811,3812],{},"Accounting:"," IFRS 17 is effective for annual periods beginning on or after 1 January 2023. It governs recognition and measurement of insurance contracts; it does not turn the deterministic chain ladder into an accounting standard.",[1800,3815,3816,3819],{},[1803,3817,3818],{},"Regulation:"," Solvency UK reporting applies for reporting dates from 31 December 2024. A classroom ruin probability is not the Solvency Capital Requirement.",[1800,3821,3822,3825],{},[1803,3823,3824],{},"Emerging loss:"," Swiss Re Institute estimated 2025 natural-catastrophe economic losses at USD 220 billion, with 49% insured, and reported that secondary perils generated 92% of insured losses. This motivates heavy-tail and dependence analysis; it does not identify a distribution by itself.",[3827,3828,3830],"h3",{"id":3829},"reading-list-provenance","Reading-list provenance",[1793,3832,3833,3834,3837],{},"The module reading lists were last checked on ",[1803,3835,3836],{},"1 August 2026",". They form a selective teaching map, not a PRISMA systematic review. Sources are used in three layers:",[1797,3839,3840,3843,3846],{},[1800,3841,3842],{},"peer-reviewed papers and established texts for mathematical foundations;",[1800,3844,3845],{},"official standard-setter and regulator pages for current institutional boundaries;",[1800,3847,3848],{},"recent professional research, data releases, and clearly labelled preprints for examples and open methods.",[1793,3850,3851],{},"Coverage is therefore illustrative rather than exhaustive. A current statistic can motivate a stress, and a preprint can motivate an extension; neither supplies a portfolio parameter without validation.",[3853,3854,3856],"warning",{"title":3855},"Evidence rule","Current industry figures are used to pose modelling questions, not to prove universal parameters. Check scope, definitions, currency, exposure, event date, publication date, and revisions before reusing any number.",[1858,3858,3860],{"id":3859},"how-to-study-and-report","How to study and report",[1793,3862,3863],{},"For every method, keep a one-page model record:",[1903,3865,3866,3876],{},[1906,3867,3868],{},[1909,3869,3870,3873],{},[1912,3871,3872],{},"Field",[1912,3874,3875],{},"Minimum answer",[1919,3877,3878,3886,3894,3902,3910,3918],{},[1909,3879,3880,3883],{},[1924,3881,3882],{},"Decision",[1924,3884,3885],{},"reserve selection, treaty comparison, or capital measure",[1909,3887,3888,3891],{},[1924,3889,3890],{},"Data",[1924,3892,3893],{},"unit, scope, valuation date, and transformations",[1909,3895,3896,3899],{},[1924,3897,3898],{},"Assumptions",[1924,3900,3901],{},"stability, independence, distribution, and contract terms",[1909,3903,3904,3907],{},[1924,3905,3906],{},"Validation",[1924,3908,3909],{},"residuals, holdout\u002Fdiagonal test, sensitivity, or simulation error",[1909,3911,3912,3915],{},[1924,3913,3914],{},"Uncertainty",[1924,3916,3917],{},"process, parameter, model, and operational sources",[1909,3919,3920,3923],{},[1924,3921,3922],{},"Boundary",[1924,3924,3925,3926,3929],{},"what the result must ",[1803,3927,3928],{},"not"," be interpreted as",[1793,3931,3932,3933,3936],{},"Start with ",[2814,3934,3935],{"href":2816},"the claims-development data contract",".",[1858,3938,3940],{"id":3939},"sources-and-further-reading","Sources and further reading",[1866,3942,3943,3951,3958,3965,3973],{},[1800,3944,3945],{},[2814,3946,3950],{"href":3947,"rel":3948},"https:\u002F\u002Fwww.ifrs.org\u002Fissued-standards\u002Flist-of-standards\u002Fifrs-17-insurance-contracts\u002F",[3949],"nofollow","IFRS Foundation — IFRS 17 Insurance Contracts",[1800,3952,3953],{},[2814,3954,3957],{"href":3955,"rel":3956},"https:\u002F\u002Fwww.bankofengland.co.uk\u002Fprudential-regulation\u002Fregulatory-reporting\u002Fregulatory-reporting-insurance-sector",[3949],"Bank of England — Solvency UK insurance-sector reporting",[1800,3959,3960],{},[2814,3961,3964],{"href":3962,"rel":3963},"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",[3949],"Swiss Re Institute — natural catastrophes in 2025",[1800,3966,3967,3968,3972],{},"Mack, T. (1993), “Distribution-Free Calculation of the Standard Error of Chain Ladder Reserve Estimates,” ",[3969,3970,3971],"em",{},"ASTIN Bulletin",", 23(2), 213–225.",[1800,3974,3975,3976,3979],{},"Klugman, S. A., Panjer, H. H., and Willmot, G. E. (2019), ",[3969,3977,3978],{},"Loss Models: From Data to Decisions",", 5th ed.",{"title":10,"searchDepth":3981,"depth":3981,"links":3982},2,[3983,3984,3985,3986,3987,3988,3989,3993,3994],{"id":1860,"depth":3981,"text":1861},{"id":1894,"depth":3981,"text":1895},{"id":2821,"depth":3981,"text":2822},{"id":3421,"depth":3981,"text":3422},{"id":3558,"depth":3981,"text":3559},{"id":3787,"depth":3981,"text":3788},{"id":3804,"depth":3981,"text":3805,"children":3990},[3991],{"id":3829,"depth":3992,"text":3830},3,{"id":3859,"depth":3981,"text":3860},{"id":3939,"depth":3981,"text":3940},"A compact, example-led course in reserving, loss models, reinsurance, aggregate risk, and ruin.","md",{"sidebar":3998},{"order":3999},0,true,{"title":830,"description":3995},"BBJt2DH5rrX5d2TGffsiZvov3cUjVT7z9tfRi25Vl3M",[4004,4006],{"title":821,"path":822,"stem":823,"description":4005,"children":-1},"Use Chart.js charts inside VitePress Markdown pages.",{"title":836,"path":837,"stem":838,"description":4007,"children":-1},"Build a defensible claims-development data contract before projecting a reserve.",1785754733991]