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Un Análisis de Sensibilidad del Proceso de Tarificación en los Seguros Generales

Author

Listed:
  • Gómez Déniz, E.

    (Universidad de Las Palmas de Gran Canaria)

  • Hernández Bastida, A.

    (Universidad de Granada)

  • Vázquez Polo, F.J.

    (Universidad de las Palmas de Gran Canaria)

Abstract

La mayoría de la literatura sobre técnicas estadisticas en la Ciencia Actuarial está basada en métodos bayesianos clásicos, en el senttido de que el actuario confía completamente en la distribución a priori del parámetro de reisgo. En este trabajo aplicacmos la metodología de la robustez bayesiana para medir la sensibilidad de la prima a posteriori (la que debe cobrarse en ese período con respecto a perturbaciones en la distribución a priori en el principio de varianza. Un camino habitual para desarrollar lo señalado consiste en desarrollar el mismo estudio bayesiano clásico respecto a la distribución a priori base ------- sobre una clase de posibles y razonables distribuciones a priori compatibles con las creencias del actuario. Usaremos la clase de e-contaminación para modelar la incertidumbre sobre la distribución a priori base. Finalmente desarrollaremos un ejemplo para ilustrar las compatibles con las creencias del actuario. Usaremos la clase de e-contaminación para modelar la incertidumbre sobre la distribución a priori base. Finalmente desarrollaremos un ejemplo para ilustrar las ideas expuestas anteriormente. Most of the Bayesian literature on statistical techniques in actuarial science are classical Bayesian methods, in the sense that the actuary is confident on the prior distribution of the risk parameter. In this paper we apply the Bayesian robust methodology to detect how sensitive the experience rated premium (the premium charged in the period) is with respect to perturbations in the prior elicitation for the variance premium charged in the period) is with respect to perturbations in the prior elicitacion for the variance premium principle. A commom way to measure this sensitivity (really local analylis) consists in developing the robustness of the posterior Bayesian analysis as the prior ranges over a class of possible and reasonable prior distributions compatible with actuary´s believes.We use e-contamination classes to model uncertainty on a given base prior ---- . An example to illustrate the above ideas is provided. Somo concluding remarks are also given.

Suggested Citation

  • Gómez Déniz, E. & Hernández Bastida, A. & Vázquez Polo, F.J., 1998. "Un Análisis de Sensibilidad del Proceso de Tarificación en los Seguros Generales," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 9, pages 19-34, Junio.
  • Handle: RePEc:lrk:eeaart:9_2_2
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    References listed on IDEAS

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    1. 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.
    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. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
    4. Makov, Udi E., 1995. "Loss robustness via Fisher-weighted squared-error loss function," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 1-6, April.
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    More about this item

    Keywords

    Risk Theory; Collective Compound Model; Variance Principle; Bayesian Robustness;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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