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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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    File URL: http://www.ugr.es/~teoriahe/RePEc/gra/fegper/FEGWP307.pdf
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    References listed on IDEAS

    as
    1. Willmot, Gord, 1986. "Mixed Compound Poisson Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 16(S1), pages 59-79, April.
    2. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    3. Hurlimann, Werner, 1990. "On maximum likelihood estimation for count data models," Insurance: Mathematics and Economics, Elsevier, vol. 9(1), pages 39-49, March.
    4. 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.
    5. Panjer, Harry H. & Willmot, Gordon E., 1983. "Compound poisson models in actuarial risk theory," Journal of Econometrics, Elsevier, vol. 23(1), pages 63-76, September.
    6. Ruohonen, Matti, 1988. "On A Model for the Claim Number Process," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 18(01), pages 57-68, April.
    7. Sundt, Bjørn & Jewell, William S., 1981. "Further Results on Recursive Evaluation of Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 12(01), pages 27-39, June.
    8. 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.
    9. Sivaganesan S., 1989. "Sensitivity Of Posterior Mean To Unimodality Preserving Contaminations," Statistics & Risk Modeling, De Gruyter, vol. 7(1-2), pages 77-94, February.
    10. repec:spr:compst:v:48:y:1998:i:1:p:117-146 is not listed on IDEAS
    11. Tremblay, Luc, 1992. "Using the Poisson Inverse Gaussian in Bonus-Malus Systems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 22(01), pages 97-106, May.
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    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Compound collective model; Bayesian analysis; Robustness analysis.;

    JEL classification:

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

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