Claims Reserving with a Robust Generalized Additive Model

Abstract

In the actuarial literature, many existing stochastic claims-reserving methods ignore the excessive effects of outliers. In practice, however, these outlying observations may occur in the upper triangle and can have a nontrivial and undesirable influence on the existing reserving models. In this article, we consider the situation when outliers of claims are present in the upper triangle. We demonstrate that the model fitting and prediction results of the classical chain-ladder method can be substantially 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 a more reliable predictive bootstrap distribution of outstanding claims. Using both simulation examples and real data, we compare our proposed robust GAM with nonrobust counterparts and robust GLM. We demonstrate that the robust GAM provides comparable results with those of other models when outliers are not present and that the robust GAM demonstrates significant improvements in estimation accuracy and efficiency when outliers are present.