Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach

We consider a model which allows data-driven threshold selection in extreme value analysis. A mixture exponential distribution is employed as the thin-tailed distribution in view of the special structure of insurance claims, where individuals are often grouped into categories. An EM algorithm-based procedure is described in model fitting. We then demonstrate how a multi-level fitting procedure will substantially reduce computation time when the data set is large. The fitted model is applied to derive statistics such as return level and expected tail loss of the claim distribution, and ruin probability bounds are obtained. Finally we propose a statistical test to justify the choice of mixture exponential distribution over the homogeneous exponential distribution in terms of improved fit.