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Applying A Bayesian Hierarchical Model In Actuarial Science: Inference And Ratemaking

In: Distribution Models Theory

Author

Listed:
  • 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)

Abstract

In 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.

Suggested Citation

  • J. M. Pérez-Sánchez & J. M. Sarabia-Alegría & E. Gómez-Déniz & F. J. Vázquez-Polo, 2006. "Applying A Bayesian Hierarchical Model In Actuarial Science: Inference And Ratemaking," World Scientific Book Chapters, in: Rafael Herrerías Pleguezuelo & José Callejón Céspedes & José Manuel Herrerías Velasco (ed.), Distribution Models Theory, chapter 13, pages 233-241, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812772992_0013
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    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;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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