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Buenos y malos riesgos en seguros: el punto de vista bayesiano basado en distribuciones bimodales

Author

Listed:
  • GÓMEZ DÉNIZ, E.

    () (Departamento de Métodos Cuantitativos en Economía y Gestión. Universidad de Las Palmas de G.C.)

  • PÉREZ SÁNCHEZ, J.M.

    () (Departamento de Métodos Cuantitativos en Economía y Gestión. Universidad de Las Palmas de G.C.)

Abstract

El modelo de buenos-malos riesgos considera que la población o colectivo de asegurados de una cartera de seguros tiene dos tipos de riesgos. Un porcentaje de ellos tiene una baja probabilidad de siniestralidad, son los buenos riesgos; mientras que el resto tiene una alta probabilidad de siniestralidad, son los malos riesgos. En esta situación, una única distribución de probabilidad no resulta lo más adecuado para modelar el proceso de siniestralidad, siendo más sugerente una combinación convexa de dos o más distribuciones. Hewitt (1.966) ha utilizado la combinación log-gamma+log-gamma; Hewitt y Lefkowitz (1.979), la combinación gamma+loggamma y gamma+log-normal; Venter (1.991) la combinación Poisson+Poisson, etc. Sin embargo, no aparecen en la literatura estudios de esta naturaleza considerados desde una perspectiva bayesiana. En este trabajo se analiza el modelo de los buenos-malos riesgos desde un punto de vista bayesiano y se realiza un análisis de robustez del mismo utilizando una clase de distribuciones a priori dada por contaminaciones de una distribución fija. Good and Bad models consider population of an insurances portfolio has two types of risks. There are good risks, which has low claims probabilities and bad risks with high claims probabilities. So we need a convex combination of two or more distributions to model this situation. Hewitt (1.966) has used combination loggamma+ log-gamma; Hewitt and Lefkowitz (1.979) used combination gamma+log-gamma and gamma+lognormal; Venter (1.991) used combination Poisson+Poisson, etc. However, bayesian methodology has not studied this model. In this work we analyzed the model of the good-bad risks from a Bayesian point of view and we will measure the sensitivity of Bayesian Premium with respect to disturbances in the prior distribution from the risk parameter using a fixed contaminated class.

Suggested Citation

  • Gómez Déniz, E. & Pérez Sánchez, J.M., 2001. "Buenos y malos riesgos en seguros: el punto de vista bayesiano basado en distribuciones bimodales," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 18, pages 175-187, Agosto.
  • Handle: RePEc:lrk:eeaart:18_2_4
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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. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
    3. Matthew E. Kahn & Siqi Zheng, 2016. "Introduction," Introductory Chapters,in: Blue Skies over Beijing:Economic Growth and the Environment in China Princeton University Press.
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    More about this item

    Keywords

    Theory of Credibility; Good and Bad Risks; Bayesian Robustness; Contaminated Class.;

    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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