Optimal and Additive Loss Reserving for Dependent Lines of Business

In the present paper we review and extend two stochastic models for loss reserving and study their impact on extensions of the additive method and of the chain-ladder method. The first of these models is a particular linear model while the second one is a sequential model which is composed of a finite number of conditional linear models. These models lead to multivariate extensions of the additive method and the chain-ladder method, respectively, which turn out to resolve the problem of additivity.