Extreme Value Analysis for Partitioned Insurance Losses

The heavy-tailed nature of insurance claims requires that special attention be put into the analysis of the tail behavior of a loss distribution. It has been demonstrated that the distribution of large claims of several lines of insurance have Pareto-type tails. As a result, estimating the tail index, which is a measure of the heavy-tailedness of a distribution, has received a great deal of attention. Although numerous tail index estimators have been proposed in the literature, many of them require detailed knowledge of individual losses and are thus inappropriate for insurance data in partitioned form. In this study we bridge this gap by developing a tail index estimator suitable for partitioned loss data. This estimator is robust in the sense that no particular global density is assumed for the loss distribution. Instead we focus only on fitting the model in the tail of the distribution where it is believed that the Pareto-type form holds. Strengths and weaknesses of the proposed estimator are explored through simulation and an application of the estimator to real world partitioned insurance data is given.