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Bayesian Analysis Of The Compound Collective Model: The Net Premium Principle With Exponential Poisson And Gamma–Gamma Distributions

Author

Listed:
  • A.Hernández-Bastida

    (Departamento de Métodos Cuantitativos para la Economía y la Empresa. Universidad de Granada(Spain))

  • J. M. Pérez–Sánchez

    (Departamento de Métodos Cuantitativos para la Economía y la Empresa. Universidad de Granada(Spain))

  • E. Gómez-Deniz

    (Department of Quantitative Methods in Economics, University of Las Palmas de G.C., Spain.)

Abstract

This article develops a Bayesian analysis of the Compound Collective Model utilizing the Net Premium Principle, considering single-period models. With respect to likelihoods, we used a Poisson distribution for the number of claims and an Exponential distribution for the severity of the accident/event. Gamma distributions were used for the prior distributions. The robustness of the posterior premium was analyzed with respect to the prior distribution specification of the severity of the accident/event, utilizing contamination classes, these being the class of all the distributions and that of all the unimodal distributions with the same mode. Numerical applications of the results obtained were performed.

Suggested Citation

  • A.Hernández-Bastida & J. M. Pérez–Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model: The Net Premium Principle With Exponential Poisson And Gamma–Gamma Distributions," FEG Working Paper Series 07/03, Faculty of Economics and Business (University of Granada).
    • Handle: RePEc:gra:fegper:07/03
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Compound collective model; Bayesian analysis; Robustness analysis.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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