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Bayesian Analysis Of The Compound Collective Model; The Variance 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))

  • M.P. Fernández-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

The distribution of the aggregate claim size is the considerable importance in insurance theory since, for example, it is needed as an input in premium calculation principles and reserve calculation which plays an important paper in ruin theory. In this paper a Bayesian study for the collective risk model by incorporating a prior distribution for both, the parameter of the claim number distribution and the parameter of the claim size distribution is made and applied to the variance premium principle. Later a sensitivity study is to carry out on both parameters using Bayesian global robustness. Despite the complicated form of the collective risk model it is shown how the robustness study can be treated in an easy way. We illustrate the results obtained with numerical examples.

Suggested Citation

  • A.Hernández-Bastida & M.P. Fernández-Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model; The Variance Premium Principle With Exponential Poisson And Gamma-Gamma Distributions," FEG Working Paper Series 07/02, Faculty of Economics and Business (University of Granada).
  • Handle: RePEc:gra:fegper:07/02
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    File URL: http://www.ugr.es/~teoriahe/RePEc/gra/fegper/FEGWP207.pdf
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    References listed on IDEAS

    as
    1. Goovaerts, M. J. & Vylder, F. De, 1979. "A Note on Iterative Premium Calculation Principles," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 10(03), pages 325-329, December.
    2. Hurlimann, Werner, 1994. "A note on experience rating, reinsurance and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 14(3), pages 197-204, July.
    3. Eichenauer, Jurgen & Lehn, Jurgen & Rettig, Stefan, 1988. "A gamma-minimax result in credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 49-57, January.
    4. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
    5. Frangos, Nicholas E. & Vrontos, Spyridon D., 2001. "Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 31(01), pages 1-22, May.
    6. Pai, Jeffrey S., 1997. "Bayesian analysis of compound loss distributions," Journal of Econometrics, Elsevier, vol. 79(1), pages 129-146, July.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bayesian Robustness; Contamination Class; Variance Principle.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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