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On the Estimation of the Credibility Factor: A Bayesian Approach*

Published online by Cambridge University Press:  29 August 2014

René Schnieper
René Schnieper*
Affiliation:
“Zürich” Versicherungs-Gesellschaft, Zürich
*
“Zürich” Versicherungs-Gesellschaft, Postfach, CH-8022 Zürich
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Abstract

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In practical applications of Credibility Theory the structure parameters usually have to be estimated from the data. This leads to an estimator of the a posteriori mean which is often biased and where the credibility factor depends on the data. A more coherent approach to the problem would be to also treat the unknown parameters as random variables and to simultaneously estimate the a posteriori mean and the structure parameters. Different statistical models are proposed which allow for such a solution. These models all lead to an estimation of the posterior mean which is a weighted average of the prior mean and of the observed mean, the weights depending on the observations.

Keywords

Credibility theoryStructure parametersStatistical estimationexponential familiesPricing of risks
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 25 , Issue 2 , November 1995 , pp. 137 - 151
Copyright
Copyright © International Actuarial Association 1995

Footnotes

*

Paper presented at the XXIVth ASTIN Colloquium in Cambridge.

References

Bühlmann, H. and Straub, E. (1970) Glaubwürdigkeit für Schadensätze. Mitteilungen der schweizerischen Vereinigung der Versicherungsmathematiker, 1970, pp. 111–113.Google Scholar
Box, G. E. P. and Tiao, G. C. (1973) Bayesian Inference in Statistical Analysis. Addison-Wesley.Google Scholar
Dubey, A. and Gisler, A. (1981) On Parameter Estimators in Credibility. Mitteilungen der schweizerischen Vereinigung der Versicherungsmathematiker, pp. 187–212.Google Scholar
Jewell, W.S. (1974) Credible Means are Exact Bayesian for Exponential Families. ASTIN Bulletin, 8.CrossRefGoogle Scholar
Jewell, W.S. and Schnieper, R. (1983) Observation-Dependent Credibility Weights. Unpublished paper presented at the Berkeley Risk Conference.Google Scholar
Klugman, S.A. (1986) Bayesian Credibility with a Noninformative Prior. Insurance and Risk Theory. Edited by Goovaerts, M., de Vylder, F. and Haezendonck, J.. Nat. ASI Series C: Mathematical and Physical Science, Vol. 171. Dordrecht, Holland: D. Reidel Publishing Company, pp. 195–206.Google Scholar