An improved estimator of the distortion risk measure for heavy-tailed claims

The main aim of this paper is to propose an alternative estimate of the distortion risk measure for heavy-tailed claims. Our approach is based on the result of Balkema and de Haan insert ignore into journalissuearticles values(1974); [3], and Pickands insert ignore into journalissuearticles values(1975); [22] for approximating the tail of the distribution by a generalized Pareto distribution. The asymptotic normality of the new estimator is established, and its performance illustrated by some results of simulation who shows the advantages of the new estimator over the estimator based on the classical extreme-value theory.