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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.

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