Prediction Error of the Multivariate Additive Loss Reserving Method for Dependent Lines of Business

Often in non-life insurance, claims reserves are the largest position on the liability side of the balance sheet. Therefore, the prediction of adequate claims reserves for a portfolio consisting of several run-off subportfolios from dependent lines of business is of big importance for every non-life insurance company. In the present paper we consider the claims reserving problem in a multivariate context, that is, we study the multivariate additive loss reserving method proposed by Hess-Schmidt-Zocher [7] and Schmidt [18]. This model allows for a simultaneous study of the individual runoff subportfolios and enables the derivation of an estimator for the conditional mean square error of prediction (MSEP) for the predictor of the ultimate claims of the total portfolio. We illustrate the results using the data from Braun [2] and show that the multivariate additive loss reserving method leads for this data set to much better results than the multivariate Chain-ladder method considered by Braun [2] and Merz-Wüthrich [14, 15].