Parameter uncertainty for extreme value distributions

Document description

The main objective of this paper is to study different levels of uncertainty that affect the premiums for high excess of loss layers when pricing risks using extreme value distributions. Using some statistical results and estimated distributions presented in McNeil (1997) for a Danish fire insurance portfolio we give price indicators for excess of loss reinsurance layers. Furthermore, we carry out a statistical analysis in order to make inferences about the premiums calculated with the estimated distributions for the underlying data set. We incorporate different levels of uncertainty that affect the premiums calculated using estimated distributions: model uncertainty, parameter uncertainty for the loss distribution and parameter uncertainty for the frequency distribution. For each level of uncertainty we simulate the distribution of the premiums for high excess of loss layers and we compare the mean of this distribution with the premium calculated using the original data set.