Generalized Mack Chain-Ladder Model of Reserving with Robust Estimation
By Przemyslaw Sloma
In this paper we consider the problem of stochastic claims reserving in the framework of development factor models (DFM). More precisely, we provide the generalized Mack chain-ladder (GMCL) model that expands the approaches of Mack (1993; 1994; 1999), Saito (2009) and Murphy, Bardis, and Majidi (2012). Our general flexible tool of reserving provides the solution to the one of the major challenges of day-to-day actuarial practice, which is quantifying the variability of reserves in the case where different methods of selecting loss developments factors (LDFs) are applied. We develop the theoretical background to estimate the conditional mean square error of prediction (MSEP) of claims reserves that is consistent with actuarial practice in selecting the LDFs. Moreover, we present an example of GMCL’s application in which we indicate how to bridge the estimation of parameters in the chain-ladder framework with the robust estimation techniques. Finally, we show how our approach can be used in validation of the reserve risk evaluation in the Solvency 2 context.
Keywords: Non-life insurance, stochastic claims reserving, Mack chain ladder, robust estimation solvency 2