Finance Department


Date of this Version


Document Type



Journal of Actuarial Practice 12 (2005), pp. 83-100


Copyright 2005 Absalom Press


We model extreme losses from an excess of loss reinsurance contract under the assumption of the existence of a subordinated process generating sequences of large claims. We characterize clusters of extreme losses and aggregate the excess losses within clusters. The number of clusters is modeled using the usual discrete probability models, and the severity of the sum of excesses within clusters is modeled using a flexible extension of the generalized Pareto distribution. We illustrate the methodology using a Danish fire insurance claims data set. Maximum likelihood point estimates and bootstrap confidence intervals are obtained for the parameters and statistical premium. The results suggest that this cluster approach may provide a better fit for the extreme tail of the annual excess losses amount when compared to classical models of risk theory.