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4.6 Empirical Bayesian credibility theory: Model 1 - the Bühlmann model.
Includes bibliographical references (p. 386-388) and index.
Table of contents Cover; Risk Modelling in General Insurance; Series Page; Title; Copyright; Contents; Preface; 1: Introduction; 1.1 The aim of this book; 1.2 Notation and prerequisites; 1.2.1 Probability; 1.2.2 Statistics; 1.2.3 Simulation; 1.2.4 The statistical software package R; 2: Models for claim numbers and claim sizes; 2.1 Distributions for claim numbers; 2.1.1 Poisson distribution; 2.1.2 Negative binomial distribution; 2.1.3 Geometric distribution; 2.1.4 Binomial distribution; 2.1.5 A summary note on R; 2.2 Distributions for claim sizes; 2.2.1 A further summary note on R. 2.2.2 Normal (Gaussian) distribution2.2.3 Exponential distribution; 2.2.4 Gamma distribution; 2.2.5 Fat-tailed distributions; 2.2.6 Lognormal distribution; 2.2.7 Pareto distribution; 2.2.8 Weibull distribution; 2.2.9 Burr distribution; 2.2.10 Loggamma distribution; 2.3 Mixture distributions; 2.4 Fitting models to claim-number and claim-size data; 2.4.1 Fitting models to claim numbers; 2.4.2 Fitting models to claim sizes; Exercises; 3: Short term risk models; 3.1 The mean and variance of a compound distribution; 3.2 The distribution of a random sum. 3.2.1 Convolution series formula for a compound distribution3.2.2 Moment generating function of a compound distribution; 3.3 Finite mixture distributions; 3.4 Special compound distributions; 3.4.1 Compound Poisson distributions; 3.4.2 Compound mixed Poisson distributions; 3.4.3 Compound negative binomial distributions; 3.4.4 Compound binomial distributions; 3.5 Numerical methods for compound distributions; 3.5.1 Panjer recursion algorithm; 3.5.2 The fast Fourier transform algorithm; 3.6 Approximations for compound distributions; 3.6.1 Approximations based on a few moments. 3.6.2 Asymptotic approximations3.7 Statistics for compound distributions; 3.8 The individual risk model; 3.8.1 The mean and variance for the individual risk model; 3.8.2 The distribution function and moment generating function for the individual risk model; 3.8.3 Approximations for the individual risk model; Exercises; 4: Model based pricing --
setting premiums; 4.1 Premium calculation principles; 4.1.1 The expected value principle (EVP); 4.1.2 The standard deviation principle (SDP); 4.1.3 The variance principle (VP); 4.1.4 The quantile principle (QP); 4.1.5 The zero utility principle (ZUP). 4.1.6 The exponential premium principle (EPP)4.1.7 Some desirable properties of premium calculation principles; 4.1.8 Other premium calculation principles; 4.2 Maximum and minimum premiums; 4.3 Introduction to credibility theory; 4.4 Bayesian estimation; 4.4.1 The posterior distribution; 4.4.2 The wider context of decision theory; 4.4.3 The binomial/beta model; 4.4.4 The Poisson/gamma model; 4.4.5 The normal/normal model; 4.5 Bayesian credibility theory; 4.5.1 Bayesian credibility estimates under the Poisson/gamma model; 4.5.2 Bayesian credibility premiums under the normal/normal model.
A wide range of topics to give students a firm foundation in statistical and actuarial concepts and their applications.