Loss reserving with kernel functions

Abstract

Loss reserving is a fundamental concept of actuarial mathematics. A traditionally used method is the chain ladder method. While it is a simple and robust method and works well in many cases, it also has its limitations. The chain ladder method is applied to aggregated data triangle, in a way similar to constructing histograms. Thus, a natural way to improve the approach is to use kernel density estimation instead. This leads to an extension called the continuous chain ladder (CCL) method. In CCL, the main choices a researcher has to make is the choice of the kernel function and the choice of bandwidth, which introduces a suitable level of smoothing. The first choice is usually made for practical or theoretical reasons and it usually has a minor impact on the performance of the estimator. However, the choice of bandwidth can significantly affect the performance of the kernel estimator. There are several possible methods suggested in the literature to choose the bandwidth. To find the optimal bandwidth, the cross-validation procedure is used. A common method for find the optimal bandwidth is the cross-validation. As it is a very time-consuming procedure, some rules of thumb that allow to skip the cross-validation step, can significantly increase the performance of CCL. In this thesis, the main goal is to find the patterns how different input scenarios affect the optimal bandwidths of the CCL model.