Credibility for the Chain Ladder Reserving Method

We consider the chain ladder reserving method in a Bayesian set up, which allows for combining individual claims development data with portfolio information as for instance development patterns from industry-wide data. We derive the Bayes estimators and the credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the exponential family with its natural conjugate priors. Finally, we make the link to classical chain ladder and show that by using a non-informative prior we arrive at the classical chain ladder forecasts. However, the estimates for the mean square error of prediction differ 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. Key-Words: Chain-Ladder, Bayes Statistics, Credibility Theory, Exponential Dispersion Family, Mean Square Error of Prediction.