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 great 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 a special case of the multivariate additive loss reserving model proposed by Hess, Schmidt, and Zocher (2006) and Schmidt (2006a). This model allows for a simultaneous study of the individual run-off 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 given in Braun (2004) and compare them to the results derived by the multivariate chain-ladder methods of Braun (2004) and Merz and Wüthrich (2008).