A Desirable Aspect in the Variance Premium in a Collective Risk Model/Un aspecto deseable de la Prima Varianza en el Modelo Colectivo de Riesgo
This paper focuses on the study of the Collective and Bayes Premiums, under the Variance Premium Principle, in the classic Collective Risk Poisson-Exponential Model. A bivariate prior distribution is considered for both the parameter of the distribution of the number of claims and that of the distribution of the claim amount, assuming independence between these parameters. Furthermore, we analyze the consequences on these premiums of small levels of contamination in the structure functions, and find that the premiums are not sensitive to small levels of uncertainty. These results extend the conclusions obtained in Gómez-Déniz et al. (2000), where only variations in the parameter for the number of claims and its effects on premiums were studied. En este trabajo se estudia un modelo colectivo de riesgo con distribución primaria una distribución de Poisson y distribución secundaria una distribución Exponencial con perfiles de riesgo (los parámetros de las anteriores distribuciones) independientes. Se calculan la Prima Colectiva y la Prima Bayes y se analiza el rango de variación de las Primas indicadas frente a contaminaciones en las funciones estructura (distribuciones a priori). Los resultados aquí obtenidos extienden los de Gómez-Déniz et al (2000), donde se consideraba un modelo solo para la variable número de reclamaciones.
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Volume (Year): 29 (2011)
Issue (Month): (Abril)
Pages: 395 (18 pags.)
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References listed on IDEAS
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- Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
- Agustin Hernandez Bastida & Emilio Gomez Deniz & Jose Maria Perez Sanchez, 2009. "Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 853-869.
- 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.
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