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Credibility for the Chain Ladder Reserving Method

Published online by Cambridge University Press:  17 April 2015

Alois Gisler  and
Mario V. Wüthrich
Alois Gisler
Affiliation:
AXA-Winterthur Insurance Company, P.O. Box 357, Email: alois.gisler@winterthur.ch
Mario V. Wüthrich
Affiliation:
Departement Mathematik, ETH Zurich, Rämistrasse 101, CH 8401 Winterthur, Email: mario.wuethrich@math.ethz.ch
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Abstract

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We consider the chain ladder reserving method in a Bayesian set up, which allows for combining the information from a specific claims development triangle with the information from a collective. That is, for instance, to consider simultaneously own company specific data and industry-wide data to estimate the own company's claims reserves. We derive Bayesian estimators and credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the exponential dispersion family with its natural conjugate priors. Finally, we make the link to the classical chain ladder method and we show that using non-informative priors we arrive at the classical chain ladder forecasts. However, the estimates for the mean square error of prediction differ in our Bayesian set up from the ones found in the literature. Hence, the paper also throws a new light upon the estimator of the mean square error of prediction of the classical chain ladder forecasts and suggests a new estimator in the chain ladder method.

Keywords

Chain LadderBayes StatisticsCredibility TheoryExponential DispersionFamilyMean Square Error of Prediction

Information

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 2 , November 2008 , pp. 565 - 600
Copyright
Copyright © ASTIN Bulletin 2008

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