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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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It uses observed loss for the developed portion and an independent prior for the unobserved portion.",[1797,1798,1800],"h2",{"id":1799},"_1-build-the-prior-ultimate","1. 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be earned premium on a consistent on-level basis and ",[1805,1913,1915,1934],{"className":1914},[1808],[1805,1916,1918],{"className":1917},[1812],[1814,1919,1920],{"xmlns":1816},[1818,1921,1922,1931],{},[1821,1923,1924],{},[1824,1925,1926,1929],{},[1827,1927,1928],{},"q",[1827,1930,1832],{},[1834,1932,1933],{"encoding":1836},"q_i",[1805,1935,1937],{"className":1936,"ariaHidden":1842},[1841],[1805,1938,1940,1944],{"className":1939},[1846],[1805,1941],{"className":1942,"style":1943},[1850],"height:0.625em;vertical-align:-0.1944em;",[1805,1945,1947,1951],{"className":1946},[1855],[1805,1948,1928],{"className":1949,"style":1950},[1855,1859],"margin-right:0.0359em;",[1805,1952,1954],{"className":1953},[1864],[1805,1955,1957,1978],{"className":1956},[1868,1869],[1805,1958,1960,1975],{"className":1959},[1873],[1805,1961,1963],{"className":1962,"style":1878},[1877],[1805,1964,1966,1969],{"style":1965},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1805,1967],{"className":1968,"style":1886},[1885],[1805,1970,1972],{"className":1971},[1890,1891,1892,1893],[1805,1973,1832],{"className":1974},[1855,1859,1893],[1805,1976,1901],{"className":1977},[1900],[1805,1979,1981],{"className":1980},[1873],[1805,1982,1984],{"className":1983,"style":1908},[1877],[1805,1985],{}," the selected expected loss ratio (ELR):",[1805,1988,1991],{"className":1989},[1990],"katex-display",[1805,1992,1994,2039],{"className":1993},[1808],[1805,1995,1997],{"className":1996},[1812],[1814,1998,2000],{"xmlns":1816,"display":1999},"block",[1818,2001,2002,2036],{},[1821,2003,2004,2016,2020,2026,2032],{},[2005,2006,2007,2010,2012],"msubsup",{},[1827,2008,2009],{},"U",[1827,2011,1832],{},[2013,2014,2015],"mtext",{},"prior",[2017,2018,2019],"mo",{},"=",[1824,2021,2022,2024],{},[1827,2023,1829],{},[1827,2025,1832],{},[1824,2027,2028,2030],{},[1827,2029,1928],{},[1827,2031,1832],{},[1827,2033,2035],{"mathvariant":2034},"normal",".",[1834,2037,2038],{"encoding":1836},"U_i^{\\text{prior}}=P_iq_i.",[1805,2040,2042,2124],{"className":2041,"ariaHidden":1842},[1841],[1805,2043,2045,2049,2112,2117,2121],{"className":2044},[1846],[1805,2046],{"className":2047,"style":2048},[1850],"height:1.2253em;vertical-align:-0.2769em;",[1805,2050,2052,2056],{"className":2051},[1855],[1805,2053,2009],{"className":2054,"style":2055},[1855,1859],"margin-right:0.109em;",[1805,2057,2059],{"className":2058},[1864],[1805,2060,2062,2103],{"className":2061},[1868,1869],[1805,2063,2065,2100],{"className":2064},[1873],[1805,2066,2069,2081],{"className":2067,"style":2068},[1877],"height:0.9484em;",[1805,2070,2072,2075],{"style":2071},"top:-2.4231em;margin-left:-0.109em;margin-right:0.05em;",[1805,2073],{"className":2074,"style":1886},[1885],[1805,2076,2078],{"className":2077},[1890,1891,1892,1893],[1805,2079,1832],{"className":2080},[1855,1859,1893],[1805,2082,2084,2087],{"style":2083},"top:-3.1809em;margin-right:0.05em;",[1805,2085],{"className":2086,"style":1886},[1885],[1805,2088,2090],{"className":2089},[1890,1891,1892,1893],[1805,2091,2093],{"className":2092},[1855,1893],[1805,2094,2097],{"className":2095},[1855,2096,1893],"text",[1805,2098,2015],{"className":2099},[1855,1893],[1805,2101,1901],{"className":2102},[1900],[1805,2104,2106],{"className":2105},[1873],[1805,2107,2110],{"className":2108,"style":2109},[1877],"height:0.2769em;",[1805,2111],{},[1805,2113],{"className":2114,"style":2116},[2115],"mspace","margin-right:0.2778em;",[1805,2118,2019],{"className":2119},[2120],"mrel",[1805,2122],{"className":2123,"style":2116},[2115],[1805,2125,2127,2131,2171,2211],{"className":2126},[1846],[1805,2128],{"className":2129,"style":2130},[1850],"height:0.8778em;vertical-align:-0.1944em;",[1805,2132,2134,2137],{"className":2133},[1855],[1805,2135,1829],{"className":2136,"style":1860},[1855,1859],[1805,2138,2140],{"className":2139},[1864],[1805,2141,2143,2163],{"className":2142},[1868,1869],[1805,2144,2146,2160],{"className":2145},[1873],[1805,2147,2149],{"className":2148,"style":1878},[1877],[1805,2150,2151,2154],{"style":1881},[1805,2152],{"className":2153,"style":1886},[1885],[1805,2155,2157],{"className":2156},[1890,1891,1892,1893],[1805,2158,1832],{"className":2159},[1855,1859,1893],[1805,2161,1901],{"className":2162},[1900],[1805,2164,2166],{"className":2165},[1873],[1805,2167,2169],{"className":2168,"style":1908},[1877],[1805,2170],{},[1805,2172,2174,2177],{"className":2173},[1855],[1805,2175,1928],{"className":2176,"style":1950},[1855,1859],[1805,2178,2180],{"className":2179},[1864],[1805,2181,2183,2203],{"className":2182},[1868,1869],[1805,2184,2186,2200],{"className":2185},[1873],[1805,2187,2189],{"className":2188,"style":1878},[1877],[1805,2190,2191,2194],{"style":1965},[1805,2192],{"className":2193,"style":1886},[1885],[1805,2195,2197],{"className":2196},[1890,1891,1892,1893],[1805,2198,1832],{"className":2199},[1855,1859,1893],[1805,2201,1901],{"className":2202},[1900],[1805,2204,2206],{"className":2205},[1873],[1805,2207,2209],{"className":2208,"style":1908},[1877],[1805,2210],{},[1805,2212,2035],{"className":2213},[1855],[1793,2215,2216],{},"For Harbour Mutual, use an 86% ELR:",[2218,2219,2220,2240],"table",{},[2221,2222,2223],"thead",{},[2224,2225,2226,2230,2234,2237],"tr",{},[2227,2228,2229],"th",{},"AY",[2227,2231,2233],{"align":2232},"right","Earned premium (£m)",[2227,2235,2236],{"align":2232},"ELR",[2227,2238,2239],{"align":2232},"Prior ultimate (£m)",[2241,2242,2243,2258,2271,2284],"tbody",{},[2224,2244,2245,2249,2252,2255],{},[2246,2247,2248],"td",{},"2020",[2246,2250,2251],{"align":2232},"324",[2246,2253,2254],{"align":2232},"86%",[2246,2256,2257],{"align":2232},"278.64",[2224,2259,2260,2263,2266,2268],{},[2246,2261,2262],{},"2021",[2246,2264,2265],{"align":2232},"365",[2246,2267,2254],{"align":2232},[2246,2269,2270],{"align":2232},"313.90",[2224,2272,2273,2276,2279,2281],{},[2246,2274,2275],{},"2022",[2246,2277,2278],{"align":2232},"380",[2246,2280,2254],{"align":2232},[2246,2282,2283],{"align":2232},"326.80",[2224,2285,2286,2289,2292,2294],{},[2246,2287,2288],{},"2023",[2246,2290,2291],{"align":2232},"580",[2246,2293,2254],{"align":2232},[2246,2295,2296],{"align":2232},"498.80",[1793,2298,2299],{},"An ELR may come from pricing, plan, exposure × frequency × severity, or comparable mature periods. “Independent” means it should not simply repackage the same immature paid losses.",[1797,2301,2303],{"id":2302},"_2-estimate-the-unobserved-proportion","2. Estimate the unobserved proportion",[1793,2305,2306,2307,2338,2339,2488],{},"From the chain-ladder CDF, the expected paid proportion at age ",[1805,2308,2310,2324],{"className":2309},[1808],[1805,2311,2313],{"className":2312},[1812],[1814,2314,2315],{"xmlns":1816},[1818,2316,2317,2322],{},[1821,2318,2319],{},[1827,2320,2321],{},"j",[1834,2323,2321],{"encoding":1836},[1805,2325,2327],{"className":2326,"ariaHidden":1842},[1841],[1805,2328,2330,2334],{"className":2329},[1846],[1805,2331],{"className":2332,"style":2333},[1850],"height:0.854em;vertical-align:-0.1944em;",[1805,2335,2321],{"className":2336,"style":2337},[1855,1859],"margin-right:0.0572em;"," is ",[1805,2340,2342,2376],{"className":2341},[1808],[1805,2343,2345],{"className":2344},[1812],[1814,2346,2347],{"xmlns":1816},[1818,2348,2349,2373],{},[1821,2350,2351,2357,2359,2363,2366],{},[1824,2352,2353,2355],{},[1827,2354,1793],{},[1827,2356,2321],{},[2017,2358,2019],{},[2360,2361,2362],"mn",{},"1",[1827,2364,2365],{"mathvariant":2034},"\u002F",[1824,2367,2368,2371],{},[1827,2369,2370],{},"F",[1827,2372,2321],{},[1834,2374,2375],{"encoding":1836},"p_j=1\u002FF_j",[1805,2377,2379,2437],{"className":2378,"ariaHidden":1842},[1841],[1805,2380,2382,2386,2428,2431,2434],{"className":2381},[1846],[1805,2383],{"className":2384,"style":2385},[1850],"height:0.7167em;vertical-align:-0.2861em;",[1805,2387,2389,2392],{"className":2388},[1855],[1805,2390,1793],{"className":2391},[1855,1859],[1805,2393,2395],{"className":2394},[1864],[1805,2396,2398,2419],{"className":2397},[1868,1869],[1805,2399,2401,2416],{"className":2400},[1873],[1805,2402,2404],{"className":2403,"style":1878},[1877],[1805,2405,2407,2410],{"style":2406},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1805,2408],{"className":2409,"style":1886},[1885],[1805,2411,2413],{"className":2412},[1890,1891,1892,1893],[1805,2414,2321],{"className":2415,"style":2337},[1855,1859,1893],[1805,2417,1901],{"className":2418},[1900],[1805,2420,2422],{"className":2421},[1873],[1805,2423,2426],{"className":2424,"style":2425},[1877],"height:0.2861em;",[1805,2427],{},[1805,2429],{"className":2430,"style":2116},[2115],[1805,2432,2019],{"className":2433},[2120],[1805,2435],{"className":2436,"style":2116},[2115],[1805,2438,2440,2444,2448],{"className":2439},[1846],[1805,2441],{"className":2442,"style":2443},[1850],"height:1.0361em;vertical-align:-0.2861em;",[1805,2445,2447],{"className":2446},[1855],"1\u002F",[1805,2449,2451,2454],{"className":2450},[1855],[1805,2452,2370],{"className":2453,"style":1860},[1855,1859],[1805,2455,2457],{"className":2456},[1864],[1805,2458,2460,2480],{"className":2459},[1868,1869],[1805,2461,2463,2477],{"className":2462},[1873],[1805,2464,2466],{"className":2465,"style":1878},[1877],[1805,2467,2468,2471],{"style":1881},[1805,2469],{"className":2470,"style":1886},[1885],[1805,2472,2474],{"className":2473},[1890,1891,1892,1893],[1805,2475,2321],{"className":2476,"style":2337},[1855,1859,1893],[1805,2478,1901],{"className":2479},[1900],[1805,2481,2483],{"className":2482},[1873],[1805,2484,2486],{"className":2485,"style":2425},[1877],[1805,2487],{},". BF assigns the prior only to the unpaid proportion:",[1805,2490,2492],{"className":2491},[1990],[1805,2493,2495,2562],{"className":2494},[1808],[1805,2496,2498],{"className":2497},[1812],[1814,2499,2500],{"xmlns":1816,"display":1999},[1818,2501,2502,2559],{},[1821,2503,2504,2524,2526,2534,2538,2540,2543,2553,2556],{},[2005,2505,2506,2515,2517],{},[2507,2508,2509,2512],"mover",{"accent":1842},[1827,2510,2511],{},"R",[2017,2513,2514],{"stretchy":1842},"^",[1827,2516,1832],{},[1821,2518,2519,2522],{},[1827,2520,2521],{},"B",[1827,2523,2370],{},[2017,2525,2019],{},[2005,2527,2528,2530,2532],{},[1827,2529,2009],{},[1827,2531,1832],{},[2013,2533,2015],{},[2017,2535,2537],{"stretchy":2536},"false","(",[2360,2539,2362],{},[2017,2541,2542],{},"−",[1824,2544,2545,2547],{},[1827,2546,1793],{},[1824,2548,2549,2551],{},[1827,2550,2321],{},[1827,2552,1832],{},[2017,2554,2555],{"stretchy":2536},")",[2017,2557,2558],{"separator":1842},",",[1834,2560,2561],{"encoding":1836},"\\widehat 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Early random payments therefore have less influence on the youngest years.",[1797,3257,3259],{"id":3258},"_3-work-the-portfolio","3. 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R_{2023}^{BF}\n=498.8\\left(1-\\frac{1}{2.8875}\\right)\n=326.06.",[1805,3448,3450,3554,3678],{"className":3449,"ariaHidden":1842},[1841],[1805,3451,3453,3456,3545,3548,3551],{"className":3452},[1846],[1805,3454],{"className":3455,"style":2571},[1850],[1805,3457,3459,3491],{"className":3458},[1855],[1805,3460,3462],{"className":3461},[1855,2578],[1805,3463,3465],{"className":3464},[1868],[1805,3466,3468],{"className":3467},[1873],[1805,3469,3471,3479],{"className":3470,"style":2588},[1877],[1805,3472,3473,3476],{"style":2591},[1805,3474],{"className":3475,"style":2595},[1885],[1805,3477,2511],{"className":3478,"style":2599},[1855,1859],[1805,3480,3482,3485],{"className":3481,"style":2604},[2603],[1805,3483],{"className":3484,"style":2595},[1885],[1805,3486,3487],{"style":2610},[2612,3488,3489],{"xmlns":2614,"width":2615,"height":2616,"viewBox":2617,"preserveAspectRatio":2618},[2620,3490],{"d":2622},[1805,3492,3494],{"className":3493},[1864],[1805,3495,3497,3537],{"className":3496},[1868,1869],[1805,3498,3500,3534],{"className":3499},[1873],[1805,3501,3503,3517],{"className":3502,"style":2635},[1877],[1805,3504,3505,3508],{"style":2638},[1805,3506],{"className":3507,"style":1886},[1885],[1805,3509,3511],{"className":3510},[1890,1891,1892,1893],[1805,3512,3514],{"className":3513},[1855,1893],[1805,3515,2288],{"className":3516},[1855,1893],[1805,3518,3519,3522],{"style":2650},[1805,3520],{"className":3521,"style":1886},[1885],[1805,3523,3525],{"className":3524},[1890,1891,1892,1893],[1805,3526,3528,3531],{"className":3527},[1855,1893],[1805,3529,2521],{"className":3530,"style":2663},[1855,1859,1893],[1805,3532,2370],{"className":3533,"style":1860},[1855,1859,1893],[1805,3535,1901],{"className":3536},[1900],[1805,3538,3540],{"className":3539},[1873],[1805,3541,3543],{"className":3542,"style":2676},[1877],[1805,3544],{},[1805,3546],{"className":3547,"style":2116},[2115],[1805,3549,2019],{"className":3550},[2120],[1805,3552],{"className":3553,"style":2116},[2115],[1805,3555,3557,3561,3564,3568,3669,3672,3675],{"className":3556},[1846],[1805,3558],{"className":3559,"style":3560},[1850],"height:2.4em;vertical-align:-0.95em;",[1805,3562,3420],{"className":3563},[1855],[1805,3565],{"className":3566,"style":3567},[2115],"margin-right:0.1667em;",[1805,3569,3572,3581,3584,3587,3590,3593,3663],{"className":3570},[3571],"minner",[1805,3573,3577],{"className":3574,"style":3576},[2754,3575],"delimcenter","top:0em;",[1805,3578,2537],{"className":3579},[3580,1892],"delimsizing",[1805,3582,2362],{"className":3583},[1855],[1805,3585],{"className":3586,"style":2761},[2115],[1805,3588,2542],{"className":3589},[2765],[1805,3591],{"className":3592,"style":2761},[2115],[1805,3594,3596,3600,3660],{"className":3595},[1855],[1805,3597],{"className":3598},[2754,3599],"nulldelimiter",[1805,3601,3603],{"className":3602},[3430],[1805,3604,3606,3651],{"className":3605},[1868,1869],[1805,3607,3609,3648],{"className":3608},[1873],[1805,3610,3613,3625,3636],{"className":3611,"style":3612},[1877],"height:1.3214em;",[1805,3614,3616,3619],{"style":3615},"top:-2.314em;",[1805,3617],{"className":3618,"style":2595},[1885],[1805,3620,3622],{"className":3621},[1855],[1805,3623,3436],{"className":3624},[1855],[1805,3626,3628,3631],{"style":3627},"top:-3.23em;",[1805,3629],{"className":3630,"style":2595},[1885],[1805,3632],{"className":3633,"style":3635},[3634],"frac-line","border-bottom-width:0.04em;",[1805,3637,3639,3642],{"style":3638},"top:-3.677em;",[1805,3640],{"className":3641,"style":2595},[1885],[1805,3643,3645],{"className":3644},[1855],[1805,3646,2362],{"className":3647},[1855],[1805,3649,1901],{"className":3650},[1900],[1805,3652,3654],{"className":3653},[1873],[1805,3655,3658],{"className":3656,"style":3657},[1877],"height:0.686em;",[1805,3659],{},[1805,3661],{"className":3662},[2864,3599],[1805,3664,3666],{"className":3665,"style":3576},[2864,3575],[1805,3667,2555],{"className":3668},[3580,1892],[1805,3670],{"className":3671,"style":2116},[2115],[1805,3673,2019],{"className":3674},[2120],[1805,3676],{"className":3677,"style":2116},[2115],[1805,3679,3681,3685],{"className":3680},[1846],[1805,3682],{"className":3683,"style":3684},[1850],"height:0.6444em;",[1805,3686,3443],{"className":3687},[1855],[1793,3689,3690],{},"The chain ladder gives £302.0m for the same year. BF is higher because pricing's prior ultimate (£498.8m) exceeds the chain-ladder ultimate (£462.0m).",[1797,3692,3694],{"id":3693},"_4-understand-the-credibility-mechanism","4. Understand the credibility mechanism",[1793,3696,3697],{},"Rewrite BF as:",[1805,3699,3701],{"className":3700},[1990],[1805,3702,3704,3806],{"className":3703},[1808],[1805,3705,3707],{"className":3706},[1812],[1814,3708,3709],{"xmlns":1816,"display":1999},[1818,3710,3711,3803],{},[1821,3712,3713,3729,3731,3737,3768,3770,3772,3774,3776,3782,3784,3801],{},[2005,3714,3715,3721,3723],{},[2507,3716,3717,3719],{"accent":1842},[1827,3718,2009],{},[2017,3720,2514],{"stretchy":1842},[1827,3722,1832],{},[1821,3724,3725,3727],{},[1827,3726,2521],{},[1827,3728,2370],{},[2017,3730,2019],{},[1824,3732,3733,3735],{},[1827,3734,1793],{},[1827,3736,1832],{},[3738,3739,3740,3765],"munder",{},[3738,3741,3742,3762],{},[1821,3743,3744,3746,3760],{},[2017,3745,2537],{"fence":1842},[3430,3747,3748,3754],{},[1824,3749,3750,3752],{},[1827,3751,2906],{},[1827,3753,1832],{},[1824,3755,3756,3758],{},[1827,3757,1793],{},[1827,3759,1832],{},[2017,3761,2555],{"fence":1842},[2017,3763,3764],{"stretchy":1842},"⏟",[2013,3766,3767],{},"chain-ladder ultimate",[2017,3769,2921],{},[2017,3771,2537],{"stretchy":2536},[2360,3773,2362],{},[2017,3775,2542],{},[1824,3777,3778,3780],{},[1827,3779,1793],{},[1827,3781,1832],{},[2017,3783,2555],{"stretchy":2536},[3738,3785,3786,3798],{},[3738,3787,3788,3796],{},[2005,3789,3790,3792,3794],{},[1827,3791,2009],{},[1827,3793,1832],{},[2013,3795,2015],{},[2017,3797,3764],{"stretchy":1842},[2013,3799,3800],{},"prior ultimate",[1827,3802,2035],{"mathvariant":2034},[1834,3804,3805],{"encoding":1836},"\\widehat U_i^{BF}\n=p_i\\underbrace{\\left(\\frac{C_i}{p_i}\\right)}_{\\text{chain-ladder ultimate}}\n+(1-p_i)\\underbrace{U_i^{\\text{prior}}}_{\\text{prior ultimate}}.",[1805,3807,3809,3910,4250,4272],{"className":3808,"ariaHidden":1842},[1841],[1805,3810,3812,3815,3901,3904,3907],{"className":3811},[1846],[1805,3813],{"className":3814,"style":2571},[1850],[1805,3816,3818,3850],{"className":3817},[1855],[1805,3819,3821],{"className":3820},[1855,2578],[1805,3822,3824],{"className":3823},[1868],[1805,3825,3827],{"className":3826},[1873],[1805,3828,3830,3838],{"className":3829,"style":2588},[1877],[1805,3831,3832,3835],{"style":2591},[1805,3833],{"className":3834,"style":2595},[1885],[1805,3836,2009],{"className":3837,"style":2055},[1855,1859],[1805,3839,3841,3844],{"className":3840,"style":2978},[2603],[1805,3842],{"className":3843,"style":2595},[1885],[1805,3845,3846],{"style":2610},[2612,3847,3848],{"xmlns":2614,"width":2615,"height":2616,"viewBox":2617,"preserveAspectRatio":2618},[2620,3849],{"d":2622},[1805,3851,3853],{"className":3852},[1864],[1805,3854,3856,3893],{"className":3855},[1868,1869],[1805,3857,3859,3890],{"className":3858},[1873],[1805,3860,3862,3873],{"className":3861,"style":2635},[1877],[1805,3863,3864,3867],{"style":3002},[1805,3865],{"className":3866,"style":1886},[1885],[1805,3868,3870],{"className":3869},[1890,1891,1892,1893],[1805,3871,1832],{"className":3872},[1855,1859,1893],[1805,3874,3875,3878],{"style":2650},[1805,3876],{"className":3877,"style":1886},[1885],[1805,3879,3881],{"className":3880},[1890,1891,1892,1893],[1805,3882,3884,3887],{"className":3883},[1855,1893],[1805,3885,2521],{"className":3886,"style":2663},[1855,1859,1893],[1805,3888,2370],{"className":3889,"style":1860},[1855,1859,1893],[1805,3891,1901],{"className":3892},[1900],[1805,3894,3896],{"className":3895},[1873],[1805,3897,3899],{"className":3898,"style":2676},[1877],[1805,3900],{},[1805,3902],{"className":3903,"style":2116},[2115],[1805,3905,2019],{"className":3906},[2120],[1805,3908],{"className":3909,"style":2116},[2115],[1805,3911,3913,3917,3957,3960,4241,4244,4247],{"className":3912},[1846],[1805,3914],{"className":3915,"style":3916},[1850],"height:3.7341em;vertical-align:-2.2841em;",[1805,3918,3920,3923],{"className":3919},[1855],[1805,3921,1793],{"className":3922},[1855,1859],[1805,3924,3926],{"className":3925},[1864],[1805,3927,3929,3949],{"className":3928},[1868,1869],[1805,3930,3932,3946],{"className":3931},[1873],[1805,3933,3935],{"className":3934,"style":1878},[1877],[1805,3936,3937,3940],{"style":2406},[1805,3938],{"className":3939,"style":1886},[1885],[1805,3941,3943],{"className":3942},[1890,1891,1892,1893],[1805,3944,1832],{"className":3945},[1855,1859,1893],[1805,3947,1901],{"className":3948},[1900],[1805,3950,3952],{"className":3951},[1873],[1805,3953,3955],{"className":3954,"style":1908},[1877],[1805,3956],{},[1805,3958],{"className":3959,"style":3567},[2115],[1805,3961,3963],{"className":3962},[3571,3738],[1805,3964,3966,4232],{"className":3965},[1868,1869],[1805,3967,3969,4229],{"className":3968},[1873],[1805,3970,3973,3992],{"className":3971,"style":3972},[1877],"height:1.45em;",[1805,3974,3976,3980],{"style":3975},"top:-1.1659em;",[1805,3977],{"className":3978,"style":3979},[1885],"height:3.45em;",[1805,3981,3983],{"className":3982},[1890,1891,1892,1893],[1805,3984,3986],{"className":3985},[1855,1893],[1805,3987,3989],{"className":3988},[1855,2096,1893],[1805,3990,3767],{"className":3991},[1855,1893],[1805,3993,3995,3998],{"style":3994},"top:-3.45em;",[1805,3996],{"className":3997,"style":3979},[1885],[1805,3999,4001],{"className":4000},[3571,3738],[1805,4002,4004,4220],{"className":4003},[1868,1869],[1805,4005,4007,4217],{"className":4006},[1873],[1805,4008,4010,4056],{"className":4009,"style":3972},[1877],[1805,4011,4014,4017],{"className":4012,"style":4013},[2603],"top:-1.852em;",[1805,4015],{"className":4016,"style":3979},[1885],[1805,4018,4022,4036,4046],{"className":4019,"style":4021},[4020],"stretchy","height:0.548em;min-width:1.6em;",[1805,4023,4027],{"className":4024,"style":4026},[4025],"brace-left","height:0.548em;",[2612,4028,4033],{"xmlns":2614,"width":4029,"height":4030,"viewBox":4031,"preserveAspectRatio":4032},"400em","0.548em","0 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",[1805,4502,4504,4522],{"className":4503},[1808],[1805,4505,4507],{"className":4506},[1812],[1814,4508,4509],{"xmlns":1816},[1818,4510,4511,4519],{},[1821,4512,4513],{},[1824,4514,4515,4517],{},[1827,4516,1793],{},[1827,4518,1832],{},[1834,4520,4521],{"encoding":1836},"p_i",[1805,4523,4525],{"className":4524,"ariaHidden":1842},[1841],[1805,4526,4528,4531],{"className":4527},[1846],[1805,4529],{"className":4530,"style":1943},[1850],[1805,4532,4534,4537],{"className":4533},[1855],[1805,4535,1793],{"className":4536},[1855,1859],[1805,4538,4540],{"className":4539},[1864],[1805,4541,4543,4563],{"className":4542},[1868,1869],[1805,4544,4546,4560],{"className":4545},[1873],[1805,4547,4549],{"className":4548,"style":1878},[1877],[1805,4550,4551,4554],{"style":2406},[1805,4552],{"className":4553,"style":1886},[1885],[1805,4555,4557],{"className":4556},[1890,1891,1892,1893],[1805,4558,1832],{"className":4559},[1855,1859,1893],[1805,4561,1901],{"className":4562},[1900],[1805,4564,4566],{"className":4565},[1873],[1805,4567,4569],{"className":4568,"style":1908},[1877],[1805,4570],{}," acts like credibility given to the chain-ladder indication:",[4573,4574,4575,4579,4582],"ul",{},[4576,4577,4578],"li",{},"at 35% paid, most weight remains on the prior;",[4576,4580,4581],{},"at 86% paid, observed experience dominates;",[4576,4583,4584],{},"at 100% paid, BF ultimate equals observed paid loss.",[1793,4586,4587],{},"This algebra explains BF more clearly than memorising a separate reserve formula.",[1797,4589,4591],{"id":4590},"_5-sensitivity-belongs-in-the-answer","5. Sensitivity belongs in the answer",[1793,4593,4594,4595,4630],{},"For a change ",[1805,4596,4598,4615],{"className":4597},[1808],[1805,4599,4601],{"className":4600},[1812],[1814,4602,4603],{"xmlns":1816},[1818,4604,4605,4612],{},[1821,4606,4607,4610],{},[1827,4608,4609],{"mathvariant":2034},"Δ",[1827,4611,1928],{},[1834,4613,4614],{"encoding":1836},"\\Delta q",[1805,4616,4618],{"className":4617,"ariaHidden":1842},[1841],[1805,4619,4621,4624,4627],{"className":4620},[1846],[1805,4622],{"className":4623,"style":2130},[1850],[1805,4625,4609],{"className":4626},[1855],[1805,4628,1928],{"className":4629,"style":1950},[1855,1859]," in ELR,",[1805,4632,4634],{"className":4633},[1990],[1805,4635,4637,4691],{"className":4636},[1808],[1805,4638,4640],{"className":4639},[1812],[1814,4641,4642],{"xmlns":1816,"display":1999},[1818,4643,4644,4688],{},[1821,4645,4646,4648,4660,4662,4668,4670,4672,4674,4680,4682,4684,4686],{},[1827,4647,4609],{"mathvariant":2034},[2005,4649,4650,4652,4654],{},[1827,4651,2511],{},[1827,4653,1832],{},[1821,4655,4656,4658],{},[1827,4657,2521],{},[1827,4659,2370],{},[2017,4661,2019],{},[1824,4663,4664,4666],{},[1827,4665,1829],{},[1827,4667,1832],{},[2017,4669,2537],{"stretchy":2536},[2360,4671,2362],{},[2017,4673,2542],{},[1824,4675,4676,4678],{},[1827,4677,1793],{},[1827,4679,1832],{},[2017,4681,2555],{"stretchy":2536},[1827,4683,4609],{"mathvariant":2034},[1827,4685,1928],{},[1827,4687,2035],{"mathvariant":2034},[1834,4689,4690],{"encoding":1836},"\\Delta R_i^{BF}=P_i(1-p_i)\\Delta q.",[1805,4692,4694,4770,4831],{"className":4693,"ariaHidden":1842},[1841],[1805,4695,4697,4701,4704,4761,4764,4767],{"className":4696},[1846],[1805,4698],{"className":4699,"style":4700},[1850],"height:1.1383em;vertical-align:-0.247em;",[1805,4702,4609],{"className":4703},[1855],[1805,4705,4707,4710],{"className":4706},[1855],[1805,4708,2511],{"className":4709,"style":2599},[1855,1859],[1805,4711,4713],{"className":4712},[1864],[1805,4714,4716,4753],{"className":4715},[1868,1869],[1805,4717,4719,4750],{"className":4718},[1873],[1805,4720,4722,4733],{"className":4721,"style":2635},[1877],[1805,4723,4724,4727],{"style":2638},[1805,4725],{"className":4726,"style":1886},[1885],[1805,4728,4730],{"className":4729},[1890,1891,1892,1893],[1805,4731,1832],{"className":4732},[1855,1859,1893],[1805,4734,4735,4738],{"style":2650},[1805,4736],{"className":4737,"style":1886},[1885],[1805,4739,4741],{"className":4740},[1890,1891,1892,1893],[1805,4742,4744,4747],{"className":4743},[1855,1893],[1805,4745,2521],{"className":4746,"style":2663},[1855,1859,1893],[1805,4748,2370],{"className":4749,"style":1860},[1855,1859,1893],[1805,4751,1901],{"className":4752},[1900],[1805,4754,4756],{"className":4755},[1873],[1805,4757,4759],{"className":4758,"style":2676},[1877],[1805,4760],{},[1805,4762],{"className":4763,"style":2116},[2115],[1805,4765,2019],{"className":4766},[2120],[1805,4768],{"className":4769,"style":2116},[2115],[1805,4771,4773,4776,4816,4819,4822,4825,4828],{"className":4772},[1846],[1805,4774],{"className":4775,"style":4256},[1850],[1805,4777,4779,4782],{"className":4778},[1855],[1805,4780,1829],{"className":4781,"style":1860},[1855,1859],[1805,4783,4785],{"className":4784},[1864],[1805,4786,4788,4808],{"className":4787},[1868,1869],[1805,4789,4791,4805],{"className":4790},[1873],[1805,4792,4794],{"className":4793,"style":1878},[1877],[1805,4795,4796,4799],{"style":1881},[1805,4797],{"className":4798,"style":1886},[1885],[1805,4800,4802],{"className":4801},[1890,1891,1892,1893],[1805,4803,1832],{"className":4804},[1855,1859,1893],[1805,4806,1901],{"className":4807},[1900],[1805,4809,4811],{"className":4810},[1873],[1805,4812,4814],{"className":4813,"style":1908},[1877],[1805,4815],{},[1805,4817,2537],{"className":4818},[2754],[1805,4820,2362],{"className":4821},[1855],[1805,4823],{"className":4824,"style":2761},[2115],[1805,4826,2542],{"className":4827},[2765],[1805,4829],{"className":4830,"style":2761},[2115],[1805,4832,4834,4837,4877,4880,4883,4886],{"className":4833},[1846],[1805,4835],{"className":4836,"style":4256},[1850],[1805,4838,4840,4843],{"className":4839},[1855],[1805,4841,1793],{"className":4842},[1855,1859],[1805,4844,4846],{"className":4845},[1864],[1805,4847,4849,4869],{"className":4848},[1868,1869],[1805,4850,4852,4866],{"className":4851},[1873],[1805,4853,4855],{"className":4854,"style":1878},[1877],[1805,4856,4857,4860],{"style":2406},[1805,4858],{"className":4859,"style":1886},[1885],[1805,4861,4863],{"className":4862},[1890,1891,1892,1893],[1805,4864,1832],{"className":4865},[1855,1859,1893],[1805,4867,1901],{"className":4868},[1900],[1805,4870,4872],{"className":4871},[1873],[1805,4873,4875],{"className":4874,"style":1908},[1877],[1805,4876],{},[1805,4878,2555],{"className":4879},[2864],[1805,4881,4609],{"className":4882},[1855],[1805,4884,1928],{"className":4885,"style":1950},[1855,1859],[1805,4887,2035],{"className":4888},[1855],[1793,4890,4891],{},"AY 2023 has premium £580m and is 34.63% paid. A five-percentage-point ELR increase changes its reserve by",[1805,4893,4895],{"className":4894},[1990],[1805,4896,4898,4945],{"className":4897},[1808],[1805,4899,4901],{"className":4900},[1812],[1814,4902,4903],{"xmlns":1816,"display":1999},[1818,4904,4905,4942],{},[1821,4906,4907,4909,4912,4914,4916,4918,4921,4923,4925,4928,4931,4934,4937,4940],{},[2360,4908,2291],{},[2017,4910,4911],{},"×",[2017,4913,2537],{"stretchy":2536},[2360,4915,2362],{},[2017,4917,2542],{},[2360,4919,4920],{},"0.3463",[2017,4922,2555],{"stretchy":2536},[2017,4924,4911],{},[2360,4926,4927],{},"0.05",[2017,4929,4930],{},"≈",[1827,4932,4933],{"mathvariant":2034},"£",[2360,4935,4936],{},"18.96",[2013,4938,4939],{},"m",[1827,4941,2035],{"mathvariant":2034},[1834,4943,4944],{"encoding":1836},"580\\times(1-0.3463)\\times0.05\\approx£18.96\\text{m}.",[1805,4946,4948,4967,4988,5009,5027],{"className":4947,"ariaHidden":1842},[1841],[1805,4949,4951,4955,4958,4961,4964],{"className":4950},[1846],[1805,4952],{"className":4953,"style":4954},[1850],"height:0.7278em;vertical-align:-0.0833em;",[1805,4956,2291],{"className":4957},[1855],[1805,4959],{"className":4960,"style":2761},[2115],[1805,4962,4911],{"className":4963},[2765],[1805,4965],{"className":4966,"style":2761},[2115],[1805,4968,4970,4973,4976,4979,4982,4985],{"className":4969},[1846],[1805,4971],{"className":4972,"style":4256},[1850],[1805,4974,2537],{"className":4975},[2754],[1805,4977,2362],{"className":4978},[1855],[1805,4980],{"className":4981,"style":2761},[2115],[1805,4983,2542],{"className":4984},[2765],[1805,4986],{"className":4987,"style":2761},[2115],[1805,4989,4991,4994,4997,5000,5003,5006],{"className":4990},[1846],[1805,4992],{"className":4993,"style":4256},[1850],[1805,4995,4920],{"className":4996},[1855],[1805,4998,2555],{"className":4999},[2864],[1805,5001],{"className":5002,"style":2761},[2115],[1805,5004,4911],{"className":5005},[2765],[1805,5007],{"className":5008,"style":2761},[2115],[1805,5010,5012,5015,5018,5021,5024],{"className":5011},[1846],[1805,5013],{"className":5014,"style":3684},[1850],[1805,5016,4927],{"className":5017},[1855],[1805,5019],{"className":5020,"style":2116},[2115],[1805,5022,4930],{"className":5023},[2120],[1805,5025],{"className":5026,"style":2116},[2115],[1805,5028,5030,5034,5038,5044],{"className":5029},[1846],[1805,5031],{"className":5032,"style":5033},[1850],"height:0.6944em;",[1805,5035,5037],{"className":5036},[1855],"£18.96",[1805,5039,5041],{"className":5040},[1855,2096],[1805,5042,4939],{"className":5043},[1855],[1805,5045,2035],{"className":5046},[1855],[1793,5048,5049],{},"Report this sensitivity rather than presenting £326.06m as if it were exact.",[1797,5051,5053],{"id":5052},"_6-when-the-method-helpsand-when-it-hides-problems","6. When the method helps—and when it hides problems",[2218,5055,5056,5069],{},[2221,5057,5058],{},[2224,5059,5060,5063,5066],{},[2227,5061,5062],{},"Situation",[2227,5064,5065],{},"BF response",[2227,5067,5068],{},"Required challenge",[2241,5070,5071,5082,5093,5104,5115],{},[2224,5072,5073,5076,5079],{},[2246,5074,5075],{},"very immature recent year",[2246,5077,5078],{},"stabilises against early random payments",[2246,5080,5081],{},"is the ELR current and on-level?",[2224,5083,5084,5087,5090],{},[2246,5085,5086],{},"exposure or rate changed",[2246,5088,5089],{},"prior can reflect new portfolio",[2246,5091,5092],{},"are premium and expected loss both adjusted consistently?",[2224,5094,5095,5098,5101],{},[2246,5096,5097],{},"large early catastrophe payment",[2246,5099,5100],{},"limits overreaction",[2246,5102,5103],{},"should the catastrophe be modelled separately?",[2224,5105,5106,5109,5112],{},[2246,5107,5108],{},"persistent adverse emergence",[2246,5110,5111],{},"gradually responds as maturity increases",[2246,5113,5114],{},"is slow response delaying recognition?",[2224,5116,5117,5120,5123],{},[2246,5118,5119],{},"weak or politically selected plan",[2246,5121,5122],{},"gives false stability",[2246,5124,5125],{},"use independent benchmarks and scenarios",[5127,5128,5130],"warning",{"title":5129},"BF is not automatically conservative","It is higher than chain ladder only when its prior for the unobserved portion is higher. A low prior can suppress genuine adverse emergence.",[1797,5132,5134],{"id":5133},"_7-cape-cod-as-the-next-idea","7. Cape Cod as the next idea",[1793,5136,5137],{},"BF takes the ELR as external. Cape Cod estimates an ELR from the triangle and exposure, broadly:",[1805,5139,5141],{"className":5140},[1990],[1805,5142,5144,5203],{"className":5143},[1808],[1805,5145,5147],{"className":5146},[1812],[1814,5148,5149],{"xmlns":1816,"display":1999},[1818,5150,5151,5200],{},[1821,5152,5153,5159,5161,5198],{},[2507,5154,5155,5157],{"accent":1842},[1827,5156,1928],{},[2017,5158,2514],{"stretchy":1842},[2017,5160,2019],{},[3430,5162,5163,5178],{},[1821,5164,5165,5172],{},[3738,5166,5167,5170],{},[2017,5168,5169],{},"∑",[1827,5171,1832],{},[1824,5173,5174,5176],{},[1827,5175,2906],{},[1827,5177,1832],{},[1821,5179,5180,5186,5192],{},[3738,5181,5182,5184],{},[2017,5183,5169],{},[1827,5185,1832],{},[1824,5187,5188,5190],{},[1827,5189,1829],{},[1827,5191,1832],{},[1824,5193,5194,5196],{},[1827,5195,1793],{},[1827,5197,1832],{},[2017,5199,2558],{"separator":1842},[1834,5201,5202],{"encoding":1836},"\\widehat q\n=\\frac{\\sum_i C_i}\n{\\sum_i P_i p_i},",[1805,5204,5206,5268],{"className":5205,"ariaHidden":1842},[1841],[1805,5207,5209,5213,5259,5262,5265],{"className":5208},[1846],[1805,5210],{"className":5211,"style":5212},[1850],"height:0.865em;vertical-align:-0.1944em;",[1805,5214,5216],{"className":5215},[1855,2578],[1805,5217,5219,5250],{"className":5218},[1868,1869],[1805,5220,5222,5247],{"className":5221},[1873],[1805,5223,5226,5234],{"className":5224,"style":5225},[1877],"height:0.6706em;",[1805,5227,5228,5231],{"style":2591},[1805,5229],{"className":5230,"style":2595},[1885],[1805,5232,1928],{"className":5233,"style":1950},[1855,1859],[1805,5235,5238,5241],{"className":5236,"style":5237},[2603],"width:calc(100% - 0.1667em);margin-left:0.1667em;top:-3.4306em;",[1805,5239],{"className":5240,"style":2595},[1885],[1805,5242,5243],{"style":2610},[2612,5244,5245],{"xmlns":2614,"width":2615,"height":2616,"viewBox":2617,"preserveAspectRatio":2618},[2620,5246],{"d":2622},[1805,5248,1901],{"className":5249},[1900],[1805,5251,5253],{"className":5252},[1873],[1805,5254,5257],{"className":5255,"style":5256},[1877],"height:0.1944em;",[1805,5258],{},[1805,5260],{"className":5261,"style":2116},[2115],[1805,5263,2019],{"className":5264},[2120],[1805,5266],{"className":5267,"style":2116},[2115],[1805,5269,5271,5275,5547],{"className":5270},[1846],[1805,5272],{"className":5273,"style":5274},[1850],"height:2.4254em;vertical-align:-0.9857em;",[1805,5276,5278,5281,5544],{"className":5277},[1855],[1805,5279],{"className":5280},[2754,3599],[1805,5282,5284],{"className":5283},[3430],[1805,5285,5287,5535],{"className":5286},[1868,1869],[1805,5288,5290,5532],{"className":5289},[1873],[1805,5291,5294,5432,5440],{"className":5292,"style":5293},[1877],"height:1.4397em;",[1805,5295,5296,5299],{"style":3615},[1805,5297],{"className":5298,"style":2595},[1885],[1805,5300,5302,5349,5352,5392],{"className":5301},[1855],[1805,5303,5306,5312],{"className":5304},[5305],"mop",[1805,5307,5169],{"className":5308,"style":5311},[5305,5309,5310],"op-symbol","small-op","position:relative;top:0em;",[1805,5313,5315],{"className":5314},[1864],[1805,5316,5318,5340],{"className":5317},[1868,1869],[1805,5319,5321,5337],{"className":5320},[1873],[1805,5322,5325],{"className":5323,"style":5324},[1877],"height:0.162em;",[1805,5326,5328,5331],{"style":5327},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1805,5329],{"className":5330,"style":1886},[1885],[1805,5332,5334],{"className":5333},[1890,1891,1892,1893],[1805,5335,1832],{"className":5336},[1855,1859,1893],[1805,5338,1901],{"className":5339},[1900],[1805,5341,5343],{"className":5342},[1873],[1805,5344,5347],{"className":5345,"style":5346},[1877],"height:0.2997em;",[1805,5348],{},[1805,5350],{"className":5351,"style":3567},[2115],[1805,5353,5355,5358],{"className":5354},[1855],[1805,5356,1829],{"className":5357,"style":1860},[1855,1859],[1805,5359,5361],{"className":5360},[1864],[1805,5362,5364,5384],{"className":5363},[1868,1869],[1805,5365,5367,5381],{"className":5366},[1873],[1805,5368,5370],{"className":5369,"style":1878},[1877],[1805,5371,5372,5375],{"style":1881},[1805,5373],{"className":5374,"style":1886},[1885],[1805,5376,5378],{"className":5377},[1890,1891,1892,1893],[1805,5379,1832],{"className":5380},[1855,1859,1893],[1805,5382,1901],{"className":5383},[1900],[1805,5385,5387],{"className":5386},[1873],[1805,5388,5390],{"className":5389,"style":1908},[1877],[1805,5391],{},[1805,5393,5395,5398],{"className":5394},[1855],[1805,5396,1793],{"className":5397},[1855,1859],[1805,5399,5401],{"className":5400},[1864],[1805,5402,5404,5424],{"className":5403},[1868,1869],[1805,5405,5407,5421],{"className":5406},[1873],[1805,5408,5410],{"className":5409,"style":1878},[1877],[1805,5411,5412,5415],{"style":2406},[1805,5413],{"className":5414,"style":1886},[1885],[1805,5416,5418],{"className":5417},[1890,1891,1892,1893],[1805,5419,1832],{"className":5420},[1855,1859,1893],[1805,5422,1901],{"className":5423},[1900],[1805,5425,5427],{"className":5426},[1873],[1805,5428,5430],{"className":5429,"style":1908},[1877],[1805,5431],{},[1805,5433,5434,5437],{"style":3627},[1805,5435],{"className":5436,"style":2595},[1885],[1805,5438],{"className":5439,"style":3635},[3634],[1805,5441,5443,5446],{"style":5442},"top:-3.6897em;",[1805,5444],{"className":5445,"style":2595},[1885],[1805,5447,5449,5489,5492],{"className":5448},[1855],[1805,5450,5452,5455],{"className":5451},[5305],[1805,5453,5169],{"className":5454,"style":5311},[5305,5309,5310],[1805,5456,5458],{"className":5457},[1864],[1805,5459,5461,5481],{"className":5460},[1868,1869],[1805,5462,5464,5478],{"className":5463},[1873],[1805,5465,5467],{"className":5466,"style":5324},[1877],[1805,5468,5469,5472],{"style":5327},[1805,5470],{"className":5471,"style":1886},[1885],[1805,5473,5475],{"className":5474},[1890,1891,1892,1893],[1805,5476,1832],{"className":5477},[1855,1859,1893],[1805,5479,1901],{"className":5480},[1900],[1805,5482,5484],{"className":5483},[1873],[1805,5485,5487],{"className":5486,"style":5346},[1877],[1805,5488],{},[1805,5490],{"className":5491,"style":3567},[2115],[1805,5493,5495,5498],{"className":5494},[1855],[1805,5496,2906],{"className":5497,"style":3062},[1855,1859],[1805,5499,5501],{"className":5500},[1864],[1805,5502,5504,5524],{"className":5503},[1868,1869],[1805,5505,5507,5521],{"className":5506},[1873],[1805,5508,5510],{"className":5509,"style":1878},[1877],[1805,5511,5512,5515],{"style":3077},[1805,5513],{"className":5514,"style":1886},[1885],[1805,5516,5518],{"className":5517},[1890,1891,1892,1893],[1805,5519,1832],{"className":5520},[1855,1859,1893],[1805,5522,1901],{"className":5523},[1900],[1805,5525,5527],{"className":5526},[1873],[1805,5528,5530],{"className":5529,"style":1908},[1877],[1805,5531],{},[1805,5533,1901],{"className":5534},[1900],[1805,5536,5538],{"className":5537},[1873],[1805,5539,5542],{"className":5540,"style":5541},[1877],"height:0.9857em;",[1805,5543],{},[1805,5545],{"className":5546},[2864,3599],[1805,5548,2558],{"className":5549},[2868],[1793,5551,5552],{},"then uses this estimated ratio in a BF-style projection. This can improve internal consistency, but it makes the prior less independent from the observed data.",[1797,5554,5556],{"id":5555},"practice","Practice",[5558,5559,5560,5563,5566],"ol",{},[4576,5561,5562],{},"A year has £200m earned premium, 75% ELR, and is 40% paid. Calculate the BF reserve.",[4576,5564,5565],{},"If £100m has already been paid, calculate BF ultimate and chain-ladder ultimate under the same 40% paid pattern.",[4576,5567,5568],{},"What happens if the early paid amount doubles but premium, ELR, and paid proportion remain fixed?",[5570,5571,5573],"legacy-details",{"title":5572},"Answers",[5558,5574,5575,5763,5934],{},[4576,5576,5577,5578,5669,5670,5762],{},"Prior ultimate ",[1805,5579,5581,5608],{"className":5580},[1808],[1805,5582,5584],{"className":5583},[1812],[1814,5585,5586],{"xmlns":1816},[1818,5587,5588,5605],{},[1821,5589,5590,5592,5595,5597,5600,5602],{},[2017,5591,2019],{},[2360,5593,5594],{},"200",[2017,5596,4911],{},[2360,5598,5599],{},"0.75",[2017,5601,2019],{},[2360,5603,5604],{},"150",[1834,5606,5607],{"encoding":1836},"=200\\times0.75=150",[1805,5609,5611,5624,5642,5660],{"className":5610,"ariaHidden":1842},[1841],[1805,5612,5614,5618,5621],{"className":5613},[1846],[1805,5615],{"className":5616,"style":5617},[1850],"height:0.3669em;",[1805,5619,2019],{"className":5620},[2120],[1805,5622],{"className":5623,"style":2116},[2115],[1805,5625,5627,5630,5633,5636,5639],{"className":5626},[1846],[1805,5628],{"className":5629,"style":4954},[1850],[1805,5631,5594],{"className":5632},[1855],[1805,5634],{"className":5635,"style":2761},[2115],[1805,5637,4911],{"className":5638},[2765],[1805,5640],{"className":5641,"style":2761},[2115],[1805,5643,5645,5648,5651,5654,5657],{"className":5644},[1846],[1805,5646],{"className":5647,"style":3684},[1850],[1805,5649,5599],{"className":5650},[1855],[1805,5652],{"className":5653,"style":2116},[2115],[1805,5655,2019],{"className":5656},[2120],[1805,5658],{"className":5659,"style":2116},[2115],[1805,5661,5663,5666],{"className":5662},[1846],[1805,5664],{"className":5665,"style":3684},[1850],[1805,5667,5604],{"className":5668},[1855],"; reserve ",[1805,5671,5673,5701],{"className":5672},[1808],[1805,5674,5676],{"className":5675},[1812],[1814,5677,5678],{"xmlns":1816},[1818,5679,5680,5698],{},[1821,5681,5682,5684,5686,5688,5691,5693,5695],{},[2017,5683,2019],{},[2360,5685,5604],{},[2017,5687,4911],{},[2360,5689,5690],{},"0.60",[2017,5692,2019],{},[1827,5694,4933],{"mathvariant":2034},[2360,5696,5697],{},"90",[1834,5699,5700],{"encoding":1836},"=150\\times0.60=£90",[1805,5702,5704,5716,5734,5752],{"className":5703,"ariaHidden":1842},[1841],[1805,5705,5707,5710,5713],{"className":5706},[1846],[1805,5708],{"className":5709,"style":5617},[1850],[1805,5711,2019],{"className":5712},[2120],[1805,5714],{"className":5715,"style":2116},[2115],[1805,5717,5719,5722,5725,5728,5731],{"className":5718},[1846],[1805,5720],{"className":5721,"style":4954},[1850],[1805,5723,5604],{"className":5724},[1855],[1805,5726],{"className":5727,"style":2761},[2115],[1805,5729,4911],{"className":5730},[2765],[1805,5732],{"className":5733,"style":2761},[2115],[1805,5735,5737,5740,5743,5746,5749],{"className":5736},[1846],[1805,5738],{"className":5739,"style":3684},[1850],[1805,5741,5690],{"className":5742},[1855],[1805,5744],{"className":5745,"style":2116},[2115],[1805,5747,2019],{"className":5748},[2120],[1805,5750],{"className":5751,"style":2116},[2115],[1805,5753,5755,5758],{"className":5754},[1846],[1805,5756],{"className":5757,"style":5033},[1850],[1805,5759,5761],{"className":5760},[1855],"£90","m.",[4576,5764,5765,5766,5858,5859,5762],{},"BF ultimate ",[1805,5767,5769,5797],{"className":5768},[1808],[1805,5770,5772],{"className":5771},[1812],[1814,5773,5774],{"xmlns":1816},[1818,5775,5776,5794],{},[1821,5777,5778,5780,5783,5785,5787,5789,5791],{},[2017,5779,2019],{},[2360,5781,5782],{},"100",[2017,5784,2921],{},[2360,5786,5697],{},[2017,5788,2019],{},[1827,5790,4933],{"mathvariant":2034},[2360,5792,5793],{},"190",[1834,5795,5796],{"encoding":1836},"=100+90=£190",[1805,5798,5800,5812,5830,5848],{"className":5799,"ariaHidden":1842},[1841],[1805,5801,5803,5806,5809],{"className":5802},[1846],[1805,5804],{"className":5805,"style":5617},[1850],[1805,5807,2019],{"className":5808},[2120],[1805,5810],{"className":5811,"style":2116},[2115],[1805,5813,5815,5818,5821,5824,5827],{"className":5814},[1846],[1805,5816],{"className":5817,"style":4954},[1850],[1805,5819,5782],{"className":5820},[1855],[1805,5822],{"className":5823,"style":2761},[2115],[1805,5825,2921],{"className":5826},[2765],[1805,5828],{"className":5829,"style":2761},[2115],[1805,5831,5833,5836,5839,5842,5845],{"className":5832},[1846],[1805,5834],{"className":5835,"style":3684},[1850],[1805,5837,5697],{"className":5838},[1855],[1805,5840],{"className":5841,"style":2116},[2115],[1805,5843,2019],{"className":5844},[2120],[1805,5846],{"className":5847,"style":2116},[2115],[1805,5849,5851,5854],{"className":5850},[1846],[1805,5852],{"className":5853,"style":5033},[1850],[1805,5855,5857],{"className":5856},[1855],"£190","m; chain-ladder ultimate ",[1805,5860,5862,5890],{"className":5861},[1808],[1805,5863,5865],{"className":5864},[1812],[1814,5866,5867],{"xmlns":1816},[1818,5868,5869,5887],{},[1821,5870,5871,5873,5875,5877,5880,5882,5884],{},[2017,5872,2019],{},[2360,5874,5782],{},[1827,5876,2365],{"mathvariant":2034},[2360,5878,5879],{},"0.40",[2017,5881,2019],{},[1827,5883,4933],{"mathvariant":2034},[2360,5885,5886],{},"250",[1834,5888,5889],{"encoding":1836},"=100\u002F0.40=£250",[1805,5891,5893,5905,5924],{"className":5892,"ariaHidden":1842},[1841],[1805,5894,5896,5899,5902],{"className":5895},[1846],[1805,5897],{"className":5898,"style":5617},[1850],[1805,5900,2019],{"className":5901},[2120],[1805,5903],{"className":5904,"style":2116},[2115],[1805,5906,5908,5911,5915,5918,5921],{"className":5907},[1846],[1805,5909],{"className":5910,"style":4256},[1850],[1805,5912,5914],{"className":5913},[1855],"100\u002F0.40",[1805,5916],{"className":5917,"style":2116},[2115],[1805,5919,2019],{"className":5920},[2120],[1805,5922],{"className":5923,"style":2116},[2115],[1805,5925,5927,5930],{"className":5926},[1846],[1805,5928],{"className":5929,"style":5033},[1850],[1805,5931,5933],{"className":5932},[1855],"£250",[4576,5935,5936],{},"BF reserve remains £90m, so BF ultimate rises only by the additional paid amount. Chain-ladder ultimate doubles. This is the intended stability—and a reason to monitor whether the prior has become stale.",[1793,5938,5939,5940,2035],{},"Next, quantify and test what the point estimates conceal in ",[5941,5942,854],"a",{"href":5943},".\u002F04-uncertainty-diagnostics",{"title":10,"searchDepth":5945,"depth":5945,"links":5946},2,[5947,5948,5949,5950,5951,5952,5953,5954],{"id":1799,"depth":5945,"text":1800},{"id":2302,"depth":5945,"text":2303},{"id":3258,"depth":5945,"text":3259},{"id":3693,"depth":5945,"text":3694},{"id":4590,"depth":5945,"text":4591},{"id":5052,"depth":5945,"text":5053},{"id":5133,"depth":5945,"text":5134},{"id":5555,"depth":5945,"text":5556},"Blend an expected-loss prior with observed maturity without letting early random payments dominate.","md",{"sidebar":5958},{"order":5959},3,true,{"title":850,"description":5955},"gQfK4GTZTSQkYbF2DqpcnHrJgrZRyjlRJQ4f3EiWHDk",[5964,5966],{"title":846,"path":847,"stem":848,"description":5965,"children":-1},"Separate claim emergence from average cost to explain why a triangle develops.",{"title":854,"path":855,"stem":856,"description":5967,"children":-1},"Distinguish process, parameter, and model uncertainty; backtest reserving assumptions.",1785754734311]