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Fijación de primas de seguros bajo técnicas de robustez bayesiana

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  • GÓMEZ DÉNIZ, E.

    ()
    (Departamento de Métodos Cuantitativos en Economía y Gestión. Universidad de Las Palmas de G.C. Fac. CC. Económicas. Módulo D. Campus de Tafira.)

  • PÉREZ SÁNCHEZ, J. M.

    ()
    (Departamento de Métodos Cuantitativos en Economía y Gestión. Universidad de Las Palmas de G.C. Fac. CC. Económicas. Módulo D. Campus de Tafira.)

Abstract

La estadística actuarial ha abordado el problema de la tarificación en los seguros de no vida desde un punto de vista clásico y bayesiano clásico. En los primeros el parámetro de riesgo se considera conocido, mientras que en los segundos se considera aleatorio. En este trabajo se estudia la prima obtenida siguiendo ambas metodologías en el modelo colectivo de la teoría del riesgo. La utilización de la metodología bayesiana supone una confianza absoluta en la distribución a priori del parámetro de riesgo, y esto ha sido ampliamente criticado por los estadísticos no bayesianos. Para salvar esta situación, y utilizando la metodología de robustez bayesiana, mediremos la sensibilidad de la prima obtenida en un contexto bayesiano con respecto a perturbaciones en la distribución a priori del parámetro de riesgo, utilizando la clase de e-contaminación. Actuarial statistics have approached tariffication problem in no-life insurances from a Bayesian and classical point of view. From the classical point of view, parameter is known, while Bayesian statistics considere it random. In this work, we studied risk premium under both methodologies in the collective model of the Risk Theory. Bayesian methodology supposes an absolute confidence in the prior distribution of the risk parameter, and it has been widely criticized by the classical statisticians. To save this situation, and using the Bayesian sensitivity methodology, we will measure the sensitivity of Bayesian Premium with respect to disturbances in the prior distribution from the risk parameter using e-contaminated class.

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Bibliographic Info

Article provided by Estudios de Economía Aplicada in its journal Estudios de Economía Aplicada.

Volume (Year): 19 (2001)
Issue (Month): (Diciembre)
Pages: 5-20

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Handle: RePEc:lrk:eeaart:19_3_13

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Keywords: Credibility Theory; Premium Calculation Principle; Bayesian Robustness; e-Contamination Class.;

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  1. Young, Virginia R., 1999. "Optimal insurance under Wang's premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 109-122, November.
  2. 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.
  3. Gomez-Deniz, E. & Hernandez-Bastida, A. & Vazquez-Polo, F. J., 1999. "The Esscher premium principle in risk theory: a Bayesian sensitivity study," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 387-395, December.
  4. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
  5. 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 Wass, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 3(1), pages 5-124, June.
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