Individual Loss Reserving with the Multivariate Skew Normal Framework

In general insurance, the evaluation of future cash flows and solvency capital has become increasingly important. To assist in this process, the present paper proposes an individual discrete-time loss reserving model describing the occurrence, the reporting delay, the time to the first payment, and the cash flows associated with the settlement process of each individual claim. The approach uses development factors similar to those of the standard chain-ladder method. These are parametrically modeled by the Multivariate Skew Normal distribution. Empirical analyses using a realistic portfolio and out-of-sample prediction tests demonstrate the relevance of the model proposed