The extended Pareto distribution as default loss model

Abstract

Many families of distributions have been proposed to describe insurance losses. The process of finding the one which results in the best fit is time consuming. This thesis tries to tackle the issue of avoiding such analyses, so that the computer can handle it on its own. The approach is to introduce a flexible default loss model which results in a good fit for most historical data. The extended Pareto distribution, which comprises both heavy-tailed Pareto distributions and light-tailed Gamma distributions, is a natural choice. The true underlying distribution might not be part of the extended Pareto family, which leads to the necessity of defining a framework for maximum likelihood estimation under misspecification. In the beginning of this thesis such a framework is defined based on asymptotic theory. Then, the possibility of using the extended Pareto family as default loss model is examined. The potential reduction in error when the parametric family is further widened is also discussed.