Reinsurance : Actuarial and Statistical Aspects.

Intro -- Title Page -- Copyright page -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 What is Reinsurance? -- 1.2 Why Reinsurance? -- 1.3 Reinsurance Data -- 1.3.1 Case Study I: Motor Liability Data -- 1.3.2 Case Study II: Dutch Fire Insurance Data -- 1.3.3 Case Study III: Austrian Storm Claim Data -- 1.3.4 Case Study IV: European Flood Risk Data -- 1.3.5 Case Study V: Groningen Earthquakes -- 1.3.6 Case Study VI: Danish Fire Insurance Data -- 1.4 Notes and Bibliography -- Chapter 2 Reinsurance Forms and their Properties -- 2.1 Quota-share Reinsurance -- 2.1.1 Some Practical Considerations -- 2.2 Surplus Reinsurance -- 2.3 Excess-of-loss Reinsurance -- 2.3.1 Moment Calculations -- 2.3.2 Reinstatements -- 2.3.3 Further Practical Considerations -- 2.4 Stop-loss Reinsurance -- 2.5 Large Claim Reinsurance -- 2.6 Combinations of Reinsurance Forms and Global Protections -- 2.7 Facultative Contracts -- 2.8 Notes and Bibliography -- Chapter 3 Models for Claim Sizes -- 3.1 Tails of Distributions -- 3.2 Large Claims -- 3.3 Common Claim Size Distributions -- 3.3.1 Light-tailed Models -- 3.3.2 Heavy-tailed Models -- 3.4 Mean Excess Analysis -- 3.5 Full Models: Splicing -- 3.6 Multivariate Modelling of Large Claims -- Chapter 4 Statistics for Claim Sizes -- 4.1 Heavy or Light Tails: QQ- and Derivative Plots -- 4.2 Large Claims Modelling through Extreme Value Analysis -- 4.2.1 EVA for Pareto-type Tails -- 4.2.2 General Tail Modelling using EVA -- 4.2.3 EVA under Upper-truncation -- 4.3 Global Fits: Splicing, Upper-truncation and Interval Censoring -- 4.3.1 Tail-mixed Erlang Splicing -- 4.3.2 Tail-mixed Erlang Splicing under Censoring and Upper-truncation -- 4.4 Incorporating Covariate Information -- 4.4.1 Pareto-type Modelling -- 4.4.2 Generalized Pareto Modelling -- 4.4.3 Regression Extremes with Censored Data.

4.5 Multivariate Analysis of Claim Distributions -- 4.5.1 The Multivariate POT Approach -- 4.5.2 Multivariate Mixtures of Erlangs -- 4.6 Estimation of Other Tail Characteristics -- 4.7 Further Case Studies -- 4.8 Notes and Bibliography -- Chapter 5 Models for Claim Counts -- 5.1 General Treatment -- 5.1.1 Main Properties of the Claim Number Process -- 5.2 The Poisson Process and its Extensions -- 5.2.1 The Homogeneous Poisson Process -- 5.2.2 Inhomogeneous Poisson Processes -- 5.2.3 Mixed Poisson Processes -- 5.2.4 Doubly Stochastic Poisson Processes -- 5.3 Other Claim Number Processes -- 5.3.1 The Nearly Mixed Poisson Model -- 5.3.2 Infinitely Divisible Processes -- 5.3.3 The Renewal Model -- 5.3.4 Markov Models -- 5.4 Discrete Claim Counts -- 5.5 Statistics of Claim Counts -- 5.5.1 Modelling Yearly Claim Counts -- 5.5.2 Modelling the Claim Arrival Process -- 5.6 Claim Numbers under Reinsurance -- 5.6.1 Number of Claims under Excess-loss Reinsurance -- 5.7 Notes and Bibliography -- Chapter 6 Total Claim Amount -- 6.1 General Formulas for Aggregating Independent Risks -- 6.2 Classical Approximations for the Total Claim Size -- 6.2.1 Approximations based on the First Few Moments -- 6.2.2 Asymptotic Approximations for Light-tailed Claims -- 6.2.3 Asymptotic Approximations for Heavy-tailed Claims -- 6.3 Panjer Recursion -- 6.4 Fast Fourier Transform -- 6.5 Total Claim Amount under Reinsurance -- 6.5.1 Proportional Reinsurance -- 6.5.2 Excess-loss Reinsurance -- 6.5.3 Stop-loss Reinsurance -- 6.6 Numerical Illustrations -- 6.7 Aggregation for Dependent Risks -- 6.8 Notes and Bibliography -- Chapter 7 Reinsurance Pricing -- 7.1 Classical Principles of Premium Calculation -- 7.2 Solvency Considerations -- 7.2.1 The Ruin Probability -- 7.2.2 One-year Time Horizon and Cost of Capital -- 7.3 Pricing Proportional Reinsurance.

7.4 Pricing Non-proportional Reinsurance -- 7.4.1 Exposure Rating -- 7.4.2 Experience Rating -- 7.4.3 Aggregate Pure Premium -- 7.5 The Aggregate Risk Margin -- 7.6 Leading and Following Reinsurers -- 7.7 Notes and Bibliography -- Chapter 8 Choice of Reinsurance -- 8.1 Decision Criteria -- 8.2 Classical Optimality Results -- 8.2.1 Pareto-optimal Risk Sharing -- 8.2.2 Stochastic Ordering -- 8.2.3 Minimizing Retained Variance -- 8.2.4 Maximizing Expected Utility -- 8.2.5 Minimizing the Ruin Probability -- 8.2.6 Combining Reinsurance Treaties over Subportfolios -- 8.3 Solvency Constraints and Cost of Capital -- 8.4 Minimizing Other Risk Measures -- 8.5 Combining Reinsurance Treaties -- 8.6 Reinsurance Chains -- 8.7 Dynamic Reinsurance -- 8.8 Beyond Piecewise Linear Contracts -- 8.9 Notes and Bibliography -- Chapter 9 Simulation -- 9.1 The Monte Carlo Method -- 9.2 Variance Reduction Techniques -- 9.2.1 Conditional Monte Carlo -- 9.2.2 Importance Sampling -- 9.2.3 Control Variates -- 9.3 Quasi-Monte Carlo Techniques -- 9.4 Notes and Bibliography -- Chapter 10 Further Topics -- 10.1 More on Large Claim Reinsurance -- 10.1.1 The Ordered Claims -- 10.1.2 Large Claim Reinsurance -- 10.1.3 ECOMOR -- 10.2 Alternative Risk Transfer -- 10.2.1 Notes and Bibliography -- 10.3 Reinsurance and Finance -- 10.4 Catastrophic Risk -- References -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.