Reinsurance : actuarial and statistical aspects / by Hansjörg Albrecher, University of Lausanne, Switzerland; Jan Beirlant, Katholieke Universiteit Leuven, BE, University of the Free State, South Africa; Jozef L. Teugels, Katholieke Universiteit Leuven, BE.
- Author:
- Albrecher, Hansjörg
- Published:
- Hoboken, NJ : John Wiley & Sons, [2017]
- Physical Description:
- 1 online resource
- Additional Creators:
- Beirlant, Jan and Teugels, Jef L.
Access Online
- Series:
- Contents:
- Machine generated contents note: 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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.
- Subject(s):
- ISBN:
- 9781119412540 (electronic bk.)
1119412544 (electronic bk.)
9781119419938
111941993X
9781119419945
1119419948
9780470772683 (cloth) - Bibliography Note:
- Includes bibliographical references and index.
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