Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions

Many different premium principles have been proposed in the literature. In this paper, we focus on the Proportional Hazard Premium. Its asymptotic normality has been established in the literature under suitable conditions which are not fulfilled in the case of heavy-tailed distributions. We thus focus on this framework and propose a reduced-bias approach for the classical estimators. A small simulation study is proposed to illustrate the efficiency of our approach.