On a Combination of Multiplicative and Additive Stochastic Loss Reserving Methods

We introduce the hybrid chain ladder (HCL) method, a distribution-free stochastic loss reserving method that allows for a weighted combination of two approaches. The first approach is data driven resembling the Chain-Ladder (CL) method. The second approach uses expert estimates of ultimate losses in a similar way as the Bornhuetter-Ferguson (BF) method. The HCL method provides a class of models that allows one to study mixtures of the two approaches. Since the CL method is susceptible to outliers whereas the BF method is very robust, mixing the two approaches becomes of practical relevance when the actuary has concerns about the quality of the data or knowledge of particular events that cause unusual effects. We give predictors for the ultimate claims and estimators for the prediction error and the uncertainty in the claims development result. An implementation of the method in an Excel spreadsheet is available at www.RiskLab.ch/hclmethod.

Keywords. Stochastic claims reserving, distribution-free method, Chain-Ladder, Bornhuetter-Ferguson, mean square error of prediction, claims development result