On univariate extreme value statistics and the estimation of reinsurance premiums

In this paper, we consider the estimation of insurance premiums for excess-of-loss reinsurance policies in excess of a high retention level. Special attention is paid to Wang’s premium principle and heavy-tailed distributions, for which estimators of small exceedance probabilities allow the estimation of reinsurance premiums. Next to the construction of estimators, we also consider the corresponding asymptotic results and illustrate the finite sample behavior through a real insurance application as well as simulations.