A Comparison of Stochastic Claims Reserving Methods

Abstract

In order to preserve their solvency, it is very important for insurance companies to accurately estimate their future required reserves. The aim of this article is to determine reserves by using different stochastic models: 1) distribution-free model (Mack's model), 2) probability distribution based models (Normal, Poisson, Gamma and Inverse Gaussian distributions), and 3) these latter probability based models combined with bootstrapping. To implement these models we used data on life-insurance and non-life insurance. Our findings indicate among distribution based methods, Mack's model (dataset 1 and 2) and Gamma probability distribution based model (dataset 3) are the best model in estimating reserves. The model based on Normal distribution produces the worst results, whatever the dataset. Regarding results of bootstrapping based on probability distribution models, they show that method based on Normal probability distribution (dataset 1 and 3) and ODP distribution (dataset 2) fit better. Our results also indicate that bootstrap method based on Chain-Ladder performs quit similarly than the best fitting probability distribution based bootstrap models. Among all retained models, methods based on bootstrapping present higher good-of-fit.