Fitting return periods for largest claims with a frechet copula: a case study

Werner Hürlimann, Suisse

Based on a four-parameter large claims distribution, which combines an exponential distribution for the lower tail with a Pareto distribution for the upper tail, the fitting of long-term empirical return periods is examined. Two distinct methods are applied. First, the return period is fitted using the univariate survival function of the large claims mix over the considered lines of business. The second method uses the bivariate large claims probability that if a pair of claims from the two lines of business occurs, then one of its components exceeds a given largest claim amount. One notes a significant underestimation of the empirical return periods when using the univariate fit of the merged multi- line business. In contrast, the fit for the bivariate Fréchet exponential Pareto distribution is rather good. To round up the study, the impact of these distinct fitting methods on the expected value of excess-of-loss contracts is analyzed
Date: 29 May - Time: 16:30 to 18:00 - Room: 251
Theme: 1.A. Stochastic dependence