Multivariate Bühlmann-Straub Credibility Model Applied to Claims Reserving for Correlated Run-off Triangles

In the present paper we consider the claims reserving problem in a multivariate context. More precisely, we apply the multivariate generalization of the well-known credibility model proposed by Bühlmann and Straub (1970) to claims reserving. This multi-variate model allows for a simultaneous study of N correlated run-off portfolios and enables the derivation of an estimator for the conditional mean square error of prediction (MSEP) for the credibility predictor of the ultimate claim of the total portfolio. Thereby, we apply multivariate credibility predictors which reflect the correlation structure between the N portfolios and which are optimal in terms of a classical optimality criterion. We illustrate the results by means of an example and compare it to the results derived by the multivariate chain-ladder method and the multivariate additive loss reserving method proposed by Merz and Wüthrich (2008a, b).