Pricing Insurance Risk: Theory and Practice

Description

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 riskAn in-depth treatment of classical risk measures and premium calculation principlesProperties of risk measures and their visualizationA logical framework for spectral and coherent risk measuresHow risk measures for capital and pricing are distinct but interactWhy the cost of capital, not capital itself, should be allocatedThe natural allocation method and how it unifies marginal and risk-adjusted probability approachesApplications 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. Pricing Insurance Risk Contents Preface 1 Introduction 1.1 Our Subject and Why It Matters 1.2 Players, Roles, and Risk Measures 1.3 Book Contents and Structure 1.4 What's in It for the Practitioner? 1.5 Where to Start 2 The Insurance Market and Our Case Studies 2.1 The Insurance Market 2.2 Ins Co.: A One-Period Insurer 2.3 Model vs. Reality 2.4 Examples and Case Studies 2.5 Learning Objectives Part I Risk 3 Risk and Risk Measures 3.1 Risk in Everyday Life 3.2 Defining Risk 3.3 Taxonomies of Risk 3.4 Representing Risk Outcomes 3.5 The Lee Diagram and Expected Losses 3.6 Risk Measures 3.7 Learning Objectives 4 Measuring Risk with Quantiles, VaR, and TVaR 4.1 Quantiles 4.2 Value at Risk 4.3 Tail VaR and Related Risk Measures 4.4 Differentiating Quantiles, VaR, and TVaR 4.5 Learning Objectives 5 Properties of Risk Measures and Advanced Topics 5.1 Probability Scenarios 5.2 Mathematical Properties of Risk Measures 5.3 Risk Preferences 5.4 The Representation Theorem for Coherent Risk Measures 5.5 Delbaen's Differentiation Theorem 5.6 Learning Objectives 5.A Lloyd's Realistic Disaster Scenarios 5.B Convergence Assumptions for Random Variables 6 Risk Measures in Practice 6.1 Selecting a Risk Measure Using the Characterization Method 6.2 Risk Measures and Risk Margins 6.3 Assessing Tail Risk in a Univariate Distribution 6.4 The Intended Purpose: Applications of Risk Measures 6.5 Compendium of Risk Measures 6.6 Learning Objectives 7 Guide to the Practice Chapters Part II Portfolio Pricing 8 Classical Portfolio Pricing Theory 8.1 Insurance Demand, Supply, and Contracts 8.2 Insurer Risk Capital 8.3 Accounting Valuation Standards 8.4 Actuarial Premium Calculation Principles and Classical Risk Theory 8.5 Investment Income in Pricing 8.6 Financial Valuation and Perfect Market Models 8.7 The Discounted Cash Flow Model 8.8 Insurance Option Pricing Models 8.9 Insurance Market Imperfections 8.10 Learning Objectives 8.A Short- and Long-Duration Contracts 8.B The Equivalence Principle 9 Classical Portfolio Pricing Practice 9.1 Stand-Alone Classical PCPs 9.2 Portfolio CCoC Pricing 9.3 Applications of Classical Risk Theory 9.4 Option Pricing Examples 9.5 Learning Objectives 10 Modern Portfolio Pricing Theory 10.1 Classical vs. Modern Pricing and Layer Pricing 10.2 Pricing with Varying Assets 10.3 Pricing by Layer and the Layer Premium Density 10.4 The Layer Premium Density as a Distortion Function 10.5 From Distortion Functions to the Insurance Market 10.6 Concave Distortion Functions 10.7 Spectral Risk Measures 10.8 Properties of an SRM and Its Associated Distortion Function 10.9 Six Representations of Spectral Risk Measures 10.10 Simulation Interpretation of Distortion Functions 10.11 Learning Objectives 10.A Technical Details 11 Modern Portfolio Pricing Practice 11.1 Applying SRMs to Discrete Random Variables 11.2 Building-Block Distortions and SRMs 11.3 Parametric Families of Distortions 11.4 SRM Pricing 11.5 Selecting a Distortion 11.6 Fitting Distortions to Cat Bond Data 11.7 Resolving an Apparent Pricing Paradox 11.8 Learning Objectives Part III Price Allocation 12 Classical Price Allocation Theory 12.1 The Allocation of Portfolio Constant CoC Pricing 12.2 Allocation of Non-Additive Functionals 12.3 Loss Payments in Default 12.4 The Historical Development of Insurance Pricing Models 12.5 Learning Objectives 13 Classical Price Allocation Practice 13.1 Allocated CCoC Pricing 13.2 Allocation of Classical PCP Pricing 13.3 Learning Objectives 14 Modern Price Allocation Theory 14.1 The Natural Allocation of a Coherent Risk Measure 14.2 Computing the Natural Allocations 14.3 A Closer Look at Unit Funding 14.4 An Axiomatic Approach to Allocation 14.5 Axiomatic Characterizations of Allocations 14.6 Learning Objectives 15 Modern Price Allocation Practice 15.1 Applying the Natural Allocations to Discrete Random Variables 15.2 Unit Funding Analysis 15.3 Bodoff's Percentile Layer of Capital Method 15.4 Case Study Exhibits 15.5 Learning Objectives Part IV Advanced Topics 16 Asset Risk 16.1 Background 16.2 Adding Asset Risk to Ins Co. 16.3 Learning Objectives 17 Reserves 17.1 Time Periods and Notation 17.2 Liability for Ultimate Losses 17.3 The Solvency II Risk Margin 17.4 Learning Objectives 18 Going Concern Franchise Value 18.1 Optimal Dividends 18.2 The Firm Life Annuity 18.3 Learning Objectives 19 Reinsurance Optimization 19.1 Background 19.2 Evaluating Ceded Reinsurance 19.3 Learning Objectives 20 Portfolio Optimization 20.1 Strategic Framework 20.2 Market Regulation 20.3 Dynamic Capital Allocation and Marginal Cost 20.4 Marginal Cost and Marginal Revenue 20.5 Performance Management and Regulatory Rigidities 20.6 Practical Implications 20.7 Learning Objectives A Background Material A.1 Interest Rate, Discount Rate, and Discount Factor A.2 Actuarial vs. Accounting Sign Conventions A.3 Probability Theory A.4 Additional Mathematical Terminology B Notation References Index ELUA