Modeling the Claims Development Result For Solvency Purposes

We assume that the claims liability process satisfies the distribution-free chain-ladder model assumptions. For claims reserving at time I we predict the total ultimate claim with the information available at time I and, similarly, at time I +1 we predict the same total ultimate claim with the (updated) information available at time I +1. The claims development result at time I +1 for accounting year (I, I +1] is then defined to be the difference between these two successive predictions for the total ultimate claim. In [6, 10] we have analyzed this claims development result and we have quantified its prediction uncertainty. Here, we simplify, modify and illustrate the results obtained in [6, 10]. We emphasize that these results have direct consequences for solvency considerations and were (under the new risk-adjusted solvency regulation) already implemented in industry.

Keywords. Stochastic Claims Reserving, Chain-Ladder Method, Claims Development Result, Loss Experience, Incurred Losses Prior Accident Years, Solvency, Mean Square Error of Prediction.