Reduced-bias estimators for the Distortion Risk Premiums for Heavy-tailed distributions

Estimation of the occurrence of extreme events actually is that of risk premiums interest in actuarial Sciences, Insurance and Finance. Heavy-tailed distributions are used to model large claims and losses. In this paper we deal with the empirical estimation of the distortion risk premiums for heavy tailed losses by using the extreme value statistics. This approach can produce a potential bias in the estimation. Thus we look at this framework here and propose a reduced-bias approach of the classical estimators already suggested in the literature. A finite sample behavior is investigated, both for simulated data and real insurance data, in order to illustrate the efficiency of our approach. Keyswords: Risk premiums · Distortion · Heavy-tailed distribution · Tail index · Extreme quantiles · Bias reduction