Individual Loss Reserving with the Multivariate Skew Normal Distribution

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses development factors similar to those of the well–known chain–ladder method. We suggest the Multivariate Skew Normal distribution as a suitable framework for modeling the multivariate distribution of development factors. Empirical analysis using a realistic portfolio and out–of–sample prediction tests demonstrate the relevance of the model proposed.