Claims Reserving with a Robust Generalized Additive Model

Abstract

Most existing stochastic claims reserving methods ignore the excessive effects of outliers. In practice, these extreme observations may occur in the upper triangle and can have a non-trivial negative influence on the existing reserving models. In this paper, we consider the situation when outliers of incurred claims are present in the upper triangle. We demonstrate that model fitting and the prediction results of the classical chain ladder method can be greatly affected by these outliers. To mitigate this negative effect, we propose a robust generalized additive model (GAM). An associated robust bootstrap based on stratified sampling is also developed to obtain more reliable predictive bootstrap distribution of outstanding claims. Using both simulation examples and real-life data, we compare our proposed robust GAM with non-robust counterparts. We demonstrate that the robust GAM provides results comparable with those of other models when outliers are not present, and that it shows significant improvements in estimation accuracy and efficiency when outliers are present.

Keywords: Stochastic claims reserving methods, Generalized additive model, Robust estimation, Robust bootstrap