Pricing insurance risk : theory and practice

著者

書誌事項

Pricing insurance risk : theory and practice

Stephen J. Mildenhall and John A. Major

(Wiley series in probability and mathematical statistics)

J. Wiley, 2022

  • : hardback

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注記

Includes bibliographical references (p. 507-522) and index

内容説明・目次

内容説明

PRICING INSURANCE RISK A comprehensive framework for measuring, valuing, and managing risk Pricing Insurance Risk: Theory and Practice delivers an accessible and authoritative account of how to determine the premium for a portfolio of non-hedgeable insurance risks and how to allocate it fairly to each portfolio component. The authors synthesize hundreds of academic research papers, bringing to light little-appreciated answers to fundamental questions about the relationships between insurance risk, capital, and premium. They lean on their industry experience throughout to connect the theory to real-world practice, such as assessing the performance of business units, evaluating risk transfer options, and optimizing portfolio mix. Readers will discover: Definitions, classifications, and specifications of risk An in-depth treatment of classical risk measures and premium calculation principles Properties of risk measures and their visualization A logical framework for spectral and coherent risk measures How risk measures for capital and pricing are distinct but interact Why the cost of capital, not capital itself, should be allocated The natural allocation method and how it unifies marginal and risk-adjusted probability approaches Applications to reserve risk, reinsurance, asset risk, franchise value, and portfolio optimization Perfect for actuaries working in the non-life or general insurance and reinsurance sectors, Pricing Insurance Risk: Theory and Practice is also an indispensable resource for banking and finance professionals, as well as risk management professionals seeking insight into measuring the value of their efforts to mitigate, transfer, or bear nonsystematic risk.

目次

Preface xii 1 Introduction 1 1.1 Our Subject and Why It Matters 1 1.2 Players, Roles, and Risk Measures 2 1.3 Book Contents and Structure 4 1.4 What's in It for the Practitioner? 7 1.5 Where to Start 9 2 The Insurance Market and Our Case Studies 13 2.1 The Insurance Market 13 2.2 Ins Co.: A One-Period Insurer 15 2.3 Model vs. Reality 16 2.4 Examples and Case Studies 17 2.5 Learning Objectives 25 Part I Risk 27 3 Risk and Risk Measures 29 3.1 Risk in Everyday Life 29 3.2 Defining Risk 30 3.3 Taxonomies of Risk 31 3.4 Representing Risk Outcomes 36 3.5 The Lee Diagram and Expected Losses 40 3.6 Risk Measures 54 3.7 Learning Objectives 60 4 Measuring Risk with Quantiles, VaR, and TVaR 63 4.1 Quantiles 63 4.2 Value at Risk 70 4.3 Tail VaR and Related Risk Measures 85 4.4 Differentiating Quantiles, VaR, and TVaR 102 4.5 Learning Objectives 102 5 Properties of Risk Measures and Advanced Topics 105 5.1 Probability Scenarios 105 5.2 Mathematical Properties of Risk Measures 110 5.3 Risk Preferences 124 5.4 The Representation Theorem for Coherent Risk Measures 130 5.5 Delbaen's Differentiation Theorem 137 5.6 Learning Objectives 141 5.A Lloyd's Realistic Disaster Scenarios 142 5.B Convergence Assumptions for Random Variables 143 6 Risk Measures in Practice 147 6.1 Selecting a Risk Measure Using the Characterization Method 147 6.2 Risk Measures and Risk Margins 148 6.3 Assessing Tail Risk in a Univariate Distribution 149 6.4 The Intended Purpose: Applications of Risk Measures 150 6.5 Compendium of Risk Measures 153 6.6 Learning Objectives 156 7 Guide to the Practice Chapters 157 Part II Portfolio Pricing 161 8 Classical Portfolio Pricing Theory 163 8.1 Insurance Demand, Supply, and Contracts 163 8.2 Insurer Risk Capital 168 8.3 Accounting Valuation Standards 178 8.4 Actuarial Premium Calculation Principles and Classical Risk Theory 182 8.5 Investment Income in Pricing 186 8.6 Financial Valuation and Perfect Market Models 189 8.7 The Discounted Cash Flow Model 192 8.8 Insurance Option Pricing Models 200 8.9 Insurance Market Imperfections 210 8.10 Learning Objectives 213 8.A Short- and Long-Duration Contracts 215 8.B The Equivalence Principle 216 9 Classical Portfolio Pricing Practice 217 9.1 Stand-Alone Classical PCPs 217 9.2 Portfolio CCoC Pricing 223 9.3 Applications of Classical Risk Theory 224 9.4 Option Pricing Examples 227 9.5 Learning Objectives 231 10 Modern Portfolio Pricing Theory 233 10.1 Classical vs. Modern Pricing and Layer Pricing 233 10.2 Pricing with Varying Assets 235 10.3 Pricing by Layer and the Layer Premium Density 238 10.4 The Layer Premium Density as a Distortion Function 239 10.5 From Distortion Functions to the Insurance Market 245 10.6 Concave Distortion Functions 252 10.7 Spectral Risk Measures 255 10.8 Properties of an SRM and Its Associated Distortion Function 259 10.9 Six Representations of Spectral Risk Measures 261 10.10 Simulation Interpretation of Distortion Functions 263 10.11 Learning Objectives 264 10.A Technical Details 265 11 Modern Portfolio Pricing Practice 271 11.1 Applying SRMs to Discrete Random Variables 271 11.2 Building-Block Distortions and SRMs 275 11.3 Parametric Families of Distortions 280 11.4 SRM Pricing 285 11.5 Selecting a Distortion 292 11.6 Fitting Distortions to Cat Bond Data 298 11.7 Resolving an Apparent Pricing Paradox 304 11.8 Learning Objectives 306 Part III Price Allocation 307 12 Classical Price Allocation Theory 309 12.1 The Allocation of Portfolio Constant CoC Pricing 309 12.2 Allocation of Non-Additive Functionals 312 12.3 Loss Payments in Default 324 12.4 The Historical Development of Insurance Pricing Models 326 12.5 Learning Objectives 337 13 Classical Price Allocation Practice 339 13.1 Allocated CCoC Pricing 339 13.2 Allocation of Classical PCP Pricing 347 13.3 Learning Objectives 348 14 Modern Price Allocation Theory 349 14.1 The Natural Allocation of a Coherent Risk Measure 349 14.2 Computing the Natural Allocations 365 14.3 A Closer Look at Unit Funding 369 14.4 An Axiomatic Approach to Allocation 385 14.5 Axiomatic Characterizations of Allocations 392 14.6 Learning Objectives 394 15 Modern Price Allocation Practice 397 15.1 Applying the Natural Allocations to Discrete Random Variables 397 15.2 Unit Funding Analysis 404 15.3 Bodoff's Percentile Layer of Capital Method 413 15.4 Case Study Exhibits 421 15.5 Learning Objectives 439 Part IV Advanced Topics 441 16 Asset Risk 443 16.1 Background 443 16.2 Adding Asset Risk to Ins Co. 444 16.3 Learning Objectives 447 17 Reserves 449 17.1 Time Periods and Notation 449 17.2 Liability for Ultimate Losses 450 17.3 The Solvency II Risk Margin 461 17.4 Learning Objectives 468 18 Going Concern Franchise Value 469 18.1 Optimal Dividends 469 18.2 The Firm Life Annuity 472 18.3 Learning Objectives 476 19 Reinsurance Optimization 477 19.1 Background 477 19.2 Evaluating Ceded Reinsurance 477 19.3 Learning Objectives 481 20 Portfolio Optimization 483 20.1 Strategic Framework 483 20.2 Market Regulation 484 20.3 Dynamic Capital Allocation and Marginal Cost 485 20.4 Marginal Cost and Marginal Revenue 487 20.5 Performance Management and Regulatory Rigidities 488 20.6 Practical Implications 490 20.7 Learning Objectives 491 A Background Material 493 A.1 Interest Rate, Discount Rate, and Discount Factor 493 A.2 Actuarial vs. Accounting Sign Conventions 493 A.3 Probability Theory 494 A.4 Additional Mathematical Terminology 500 B Notation 503 References 507 Index 523

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