Approximation of the Equilibrium Distribution via Extreme Value Theory: an Application to Insurance Risk

We use the excess over a threshold method (see e.g. Embrechts et al. 1997 ) to approximate the tails of equilibrium distributions (integrated tail distributions) associated to distributions with regularly varying tail. We evaluate the performance of our approximations in some particular cases of distributions with regularly varying tails. Finally, we apply our results to the Danish reinsurance real data set.