Risk theory.
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| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer,
2018.
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| Series: | Springer actuarial lecture notes.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Intro; Preface; Contents; Principal Notation; 1 Risk Models; 1.1 Introduction; 1.2 The Compound Binomial Model; 1.3 The Compound Poisson Model; 1.4 The Compound Mixed Poisson Model; 1.5 The Compound Negative Binomial Model; 1.6 A Note on the Individual Model; 1.7 A Note on Reinsurance; 1.7.1 Proportional Reinsurance; 1.7.2 Excess of Loss Reinsurance; 1.8 Computation of the Distribution of S in the Discrete Case; 1.9 Approximations to S; 1.9.1 The Normal Approximation; 1.9.2 The Translated Gamma Approximation; 1.9.3 The Edgeworth Approximation; 1.9.4 The Normal Power Approximation
- 1.10 Premium Calculation Principles1.10.1 The Expected Value Principle; 1.10.2 The Variance Principle; 1.10.3 The Standard Deviation Principle; 1.10.4 The Modified Variance Principle; 1.10.5 The Principle of Zero Utility; 1.10.6 The Mean Value Principle; 1.10.7 The Exponential Principle; 1.10.8 The Esscher Principle; 1.10.9 The Distortion Principle; 1.10.10 The Percentage Principle; 1.10.11 Desirable Properties; 1.11 Risk Measures; 1.11.1 Introduction; 1.11.2 Representation of Convex and Coherent Risk Measures; 2 Utility Theory; 2.1 The Expected Utility Hypothesis
- 2.2 The Zero Utility Premium2.3 Optimal Insurance; 2.4 The Position of the Insurer; 2.5 Pareto-Optimal Risk Exchanges; 3 Credibility Theory; 3.1 Introduction; 3.2 Bayesian Credibility; 3.2.1 The Poisson-Gamma Model; 3.2.2 The Normal-Normal Model; 3.2.3 Is the Credibility Premium Formula Always Linear?; 3.3 Empirical Bayes Credibility; 3.3.1 The Bühlmann Model; 3.3.2 The Bühlmann-Straub Model; 3.3.3 The Bühlmann-Straub Model with Missing Data; 3.4 General Bayes Methods; 3.5 Hilbert Space Methods; 3.6 Bonus-Malus Systems; 4 Claims Reserving; 4.1 Introduction
- 4.2 Classical Claims Reserving Methods4.2.1 The Chain-Ladder Method; 4.2.2 The Loss-Development Method; 4.2.3 The Additive Method; 4.2.4 The Cape Cod Method; 4.2.5 The Bornhuetter-Ferguson Method; 4.2.6 The Cross-Classified Model; 4.3 The Dirichlet Model; 5 The Cramér-Lundberg Model; 5.1 Definition of the Cramér-Lundberg Process; 5.2 A Note on the Model and Reality; 5.3 A Differential Equation for the Ruin Probability; 5.4 The Adjustment Coefficient; 5.5 Lundberg's Inequality; 5.6 The Cramér-Lundberg Approximation; 5.7 Reinsurance and Ruin; 5.7.1 Proportional Reinsurance