APPLYING A BAYESIAN HIERARCHICAL MODEL IN ACTUARIAL SCIENCE: INFERENCE AND RATEMAKING

J. M. Pérez-Sánchez, J. M. Sarabia-Alegría, E. Gómez-Déniz and F. J. Vázquez-Polo
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J. M. Pérez-Sánchez: Department of Quantitative Methods in Economics, University of Granada, 18071-Granada, Spain
J. M. Sarabia-Alegría: Department of Economics, University of Cantabria, 39005-Santander, Spain
E. Gómez-Déniz: Department of Quantitative Methods in Economics, University of Las Palmas de Gran Canaria, 35017-Las Palmas de G.C., Spain
F. J. Vázquez-Polo: Department of Quantitative Methods in Economics, University of Las Palmas de Gran Canaria, 35017-Las Palmas de G. C., Spain

Chapter 13 in Distribution Models Theory, 2006, pp 233-241 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn a standard Bayesian model, a prior distribution is elicited for the structure parameter in order to obtain an estimate of this unknown parameter. The hierarchical model is a two way Bayesian one which incorporates a hyperprior distribution for some of the hyperparameters of the prior. In this way and under the Poisson-Gamma-Gamma model, a new distribution is obtained by computing the unconditional distribution of the random variable of interest. This distribution seems to provide a better fit to the data, given a policyholders' portfolio. Furthermore, Bayes premiums are thus obtained under a bonus-malus system and solve some of the problems of surcharges which appear in these systems when they are applied in a simple manner.

Keywords: Inference; Uncertainty; Copulas; Stochastic Dominance; Bayesian Techniques; Hierarchical Bayesian Model; Poisson-Gamma-Gamma Model; Experience Rating; Specific Fecundity Rates; Fecundity Curves; Topp and Leone Distributions; Waring Distribution; Factorial; Cluster; Discrimination Analyses; Survival Functions (search for similar items in EconPapers)
JEL-codes: C5 C7 (search for similar items in EconPapers)
Date: 2006
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