Credibility for the Chain Ladder Reserving Method release_kz7yot4i6rgjzk7krfq7c6zz4i

by Alois Gisler, Mario V. Wüthrich

Published in ASTIN Bulletin: The Journal of the International Actuarial Association by Cambridge University Press (CUP).

2008   Volume 38, Issue 02, p565-600

Abstract

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.
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