{"product_id":"pricing-insurance-risk-9781119755678","title":"Pricing Insurance Risk","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePRICING 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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Our Subject and Why It Matters 1\u003c\/p\u003e \u003cp\u003e1.2 Players, Roles, and Risk Measures 2\u003c\/p\u003e \u003cp\u003e1.3 Book Contents and Structure 4\u003c\/p\u003e \u003cp\u003e1.4 What’s in It for the Practitioner? 7\u003c\/p\u003e \u003cp\u003e1.5 Where to Start 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Insurance Market and Our Case Studies 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Insurance Market 13\u003c\/p\u003e \u003cp\u003e2.2 Ins Co.: A One-Period Insurer 15\u003c\/p\u003e \u003cp\u003e2.3 Model vs. Reality 16\u003c\/p\u003e \u003cp\u003e2.4 Examples and Case Studies 17\u003c\/p\u003e \u003cp\u003e2.5 Learning Objectives 25\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Risk 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Risk and Risk Measures 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Risk in Everyday Life 29\u003c\/p\u003e \u003cp\u003e3.2 Defining Risk 30\u003c\/p\u003e \u003cp\u003e3.3 Taxonomies of Risk 31\u003c\/p\u003e \u003cp\u003e3.4 Representing Risk Outcomes 36\u003c\/p\u003e \u003cp\u003e3.5 The Lee Diagram and Expected Losses 40\u003c\/p\u003e \u003cp\u003e3.6 Risk Measures 54\u003c\/p\u003e \u003cp\u003e3.7 Learning Objectives 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Measuring Risk with Quantiles, VaR, and TVaR 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Quantiles 63\u003c\/p\u003e \u003cp\u003e4.2 Value at Risk 70\u003c\/p\u003e \u003cp\u003e4.3 Tail VaR and Related Risk Measures 85\u003c\/p\u003e \u003cp\u003e4.4 Differentiating Quantiles, VaR, and TVaR 102\u003c\/p\u003e \u003cp\u003e4.5 Learning Objectives 102\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Properties of Risk Measures and Advanced Topics 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Probability Scenarios 105\u003c\/p\u003e \u003cp\u003e5.2 Mathematical Properties of Risk Measures 110\u003c\/p\u003e \u003cp\u003e5.3 Risk Preferences 124\u003c\/p\u003e \u003cp\u003e5.4 The Representation Theorem for Coherent Risk Measures 130\u003c\/p\u003e \u003cp\u003e5.5 Delbaen’s Differentiation Theorem 137\u003c\/p\u003e \u003cp\u003e5.6 Learning Objectives 141\u003c\/p\u003e \u003cp\u003e5.A Lloyd’s Realistic Disaster Scenarios 142\u003c\/p\u003e \u003cp\u003e5.B Convergence Assumptions for Random Variables 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Risk Measures in Practice 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Selecting a Risk Measure Using the Characterization Method 147\u003c\/p\u003e \u003cp\u003e6.2 Risk Measures and Risk Margins 148\u003c\/p\u003e \u003cp\u003e6.3 Assessing Tail Risk in a Univariate Distribution 149\u003c\/p\u003e \u003cp\u003e6.4 The Intended Purpose: Applications of Risk Measures 150\u003c\/p\u003e \u003cp\u003e6.5 Compendium of Risk Measures 153\u003c\/p\u003e \u003cp\u003e6.6 Learning Objectives 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Guide to the Practice Chapters 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Portfolio Pricing 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Classical Portfolio Pricing Theory 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Insurance Demand, Supply, and Contracts 163\u003c\/p\u003e \u003cp\u003e8.2 Insurer Risk Capital 168\u003c\/p\u003e \u003cp\u003e8.3 Accounting Valuation Standards 178\u003c\/p\u003e \u003cp\u003e8.4 Actuarial Premium Calculation Principles and Classical Risk Theory 182\u003c\/p\u003e \u003cp\u003e8.5 Investment Income in Pricing 186\u003c\/p\u003e \u003cp\u003e8.6 Financial Valuation and Perfect Market Models 189\u003c\/p\u003e \u003cp\u003e8.7 The Discounted Cash Flow Model 192\u003c\/p\u003e \u003cp\u003e8.8 Insurance Option Pricing Models 200\u003c\/p\u003e \u003cp\u003e8.9 Insurance Market Imperfections 210\u003c\/p\u003e \u003cp\u003e8.10 Learning Objectives 213\u003c\/p\u003e \u003cp\u003e8.A Short- and Long-Duration Contracts 215\u003c\/p\u003e \u003cp\u003e8.B The Equivalence Principle 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Classical Portfolio Pricing Practice 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Stand-Alone Classical PCPs 217\u003c\/p\u003e \u003cp\u003e9.2 Portfolio CCoC Pricing 223\u003c\/p\u003e \u003cp\u003e9.3 Applications of Classical Risk Theory 224\u003c\/p\u003e \u003cp\u003e9.4 Option Pricing Examples 227\u003c\/p\u003e \u003cp\u003e9.5 Learning Objectives 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Modern Portfolio Pricing Theory 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Classical vs. Modern Pricing and Layer Pricing 233\u003c\/p\u003e \u003cp\u003e10.2 Pricing with Varying Assets 235\u003c\/p\u003e \u003cp\u003e10.3 Pricing by Layer and the Layer Premium Density 238\u003c\/p\u003e \u003cp\u003e10.4 The Layer Premium Density as a Distortion Function 239\u003c\/p\u003e \u003cp\u003e10.5 From Distortion Functions to the Insurance Market 245\u003c\/p\u003e \u003cp\u003e10.6 Concave Distortion Functions 252\u003c\/p\u003e \u003cp\u003e10.7 Spectral Risk Measures 255\u003c\/p\u003e \u003cp\u003e10.8 Properties of an SRM and Its Associated Distortion Function 259\u003c\/p\u003e \u003cp\u003e10.9 Six Representations of Spectral Risk Measures 261\u003c\/p\u003e \u003cp\u003e10.10 Simulation Interpretation of Distortion Functions 263\u003c\/p\u003e \u003cp\u003e10.11 Learning Objectives 264\u003c\/p\u003e \u003cp\u003e10.A Technical Details 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Modern Portfolio Pricing Practice 271\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Applying SRMs to Discrete Random Variables 271\u003c\/p\u003e \u003cp\u003e11.2 Building-Block Distortions and SRMs 275\u003c\/p\u003e \u003cp\u003e11.3 Parametric Families of Distortions 280\u003c\/p\u003e \u003cp\u003e11.4 SRM Pricing 285\u003c\/p\u003e \u003cp\u003e11.5 Selecting a Distortion 292\u003c\/p\u003e \u003cp\u003e11.6 Fitting Distortions to Cat Bond Data 298\u003c\/p\u003e \u003cp\u003e11.7 Resolving an Apparent Pricing Paradox 304\u003c\/p\u003e \u003cp\u003e11.8 Learning Objectives 306\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Price Allocation 307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Classical Price Allocation Theory 309\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The Allocation of Portfolio Constant CoC Pricing 309\u003c\/p\u003e \u003cp\u003e12.2 Allocation of Non-Additive Functionals 312\u003c\/p\u003e \u003cp\u003e12.3 Loss Payments in Default 324\u003c\/p\u003e \u003cp\u003e12.4 The Historical Development of Insurance Pricing Models 326\u003c\/p\u003e \u003cp\u003e12.5 Learning Objectives 337\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Classical Price Allocation Practice 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Allocated CCoC Pricing 339\u003c\/p\u003e \u003cp\u003e13.2 Allocation of Classical PCP Pricing 347\u003c\/p\u003e \u003cp\u003e13.3 Learning Objectives 348\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Modern Price Allocation Theory 349\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 The Natural Allocation of a Coherent Risk Measure 349\u003c\/p\u003e \u003cp\u003e14.2 Computing the Natural Allocations 365\u003c\/p\u003e \u003cp\u003e14.3 A Closer Look at Unit Funding 369\u003c\/p\u003e \u003cp\u003e14.4 An Axiomatic Approach to Allocation 385\u003c\/p\u003e \u003cp\u003e14.5 Axiomatic Characterizations of Allocations 392\u003c\/p\u003e \u003cp\u003e14.6 Learning Objectives 394\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Modern Price Allocation Practice 397\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Applying the Natural Allocations to Discrete Random Variables 397\u003c\/p\u003e \u003cp\u003e15.2 Unit Funding Analysis 404\u003c\/p\u003e \u003cp\u003e15.3 Bodoff’s Percentile Layer of Capital Method 413\u003c\/p\u003e \u003cp\u003e15.4 Case Study Exhibits 421\u003c\/p\u003e \u003cp\u003e15.5 Learning Objectives 439\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Advanced Topics 441\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Asset Risk 443\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Background 443\u003c\/p\u003e \u003cp\u003e16.2 Adding Asset Risk to Ins Co. 444\u003c\/p\u003e \u003cp\u003e16.3 Learning Objectives 447\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Reserves 449\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Time Periods and Notation 449\u003c\/p\u003e \u003cp\u003e17.2 Liability for Ultimate Losses 450\u003c\/p\u003e \u003cp\u003e17.3 The Solvency II Risk Margin 461\u003c\/p\u003e \u003cp\u003e17.4 Learning Objectives 468\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Going Concern Franchise Value 469\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Optimal Dividends 469\u003c\/p\u003e \u003cp\u003e18.2 The Firm Life Annuity 472\u003c\/p\u003e \u003cp\u003e18.3 Learning Objectives 476\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Reinsurance Optimization 477\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Background 477\u003c\/p\u003e \u003cp\u003e19.2 Evaluating Ceded Reinsurance 477\u003c\/p\u003e \u003cp\u003e19.3 Learning Objectives 481\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Portfolio Optimization 483\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Strategic Framework 483\u003c\/p\u003e \u003cp\u003e20.2 Market Regulation 484\u003c\/p\u003e \u003cp\u003e20.3 Dynamic Capital Allocation and Marginal Cost 485\u003c\/p\u003e \u003cp\u003e20.4 Marginal Cost and Marginal Revenue 487\u003c\/p\u003e \u003cp\u003e20.5 Performance Management and Regulatory Rigidities 488\u003c\/p\u003e \u003cp\u003e20.6 Practical Implications 490\u003c\/p\u003e \u003cp\u003e20.7 Learning Objectives 491\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Background Material 493\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Interest Rate, Discount Rate, and Discount Factor 493\u003c\/p\u003e \u003cp\u003eA.2 Actuarial vs. Accounting Sign Conventions 493\u003c\/p\u003e \u003cp\u003eA.3 Probability Theory 494\u003c\/p\u003e \u003cp\u003eA.4 Additional Mathematical Terminology 500\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Notation 503\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 507\u003c\/p\u003e \u003cp\u003eIndex 523\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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