Combining Chain-Ladder and Additive Loss Reserving Methods for Dependent Lines of Business

Often in non-life insurance, claim reserves are the largest position on the liability side of the balance sheet. Therefore, the estimation of adequate claim reserves for a portfolio consisting of several run-off subportfolios is relevant for every non-life insurance company. In the present paper we provide a framework in which we unify the multivariate chain-ladder (CL) model and the multivariate additive loss reserving (ALR) model into one model. This model allows for the simultaneous study of individual run-off subportfolios in which we use both the CL method and the ALR method for different subportfolios. Moreover, we derive an estimator for the conditional mean square error of prediction (MSEP) for the predictor of the ultimate claims of the total portfolio.