Bias reduction in risk modelling: Semi-parametric quantile estimation

InStatistics of Extremes we are mainly interested in the estimation of quantities related to extreme events. In many areas of application, like for instanceInsurance Mathematics, Finance andStatistical Quality Control, a typical requirement is to find a value, high enough, so that the chance of an exceedance of that value is small. We are then interested in the estimation of ahigh quantile Xp, a value which is overpassed with a small probabilityp. In this paper we deal with the semi-parametric estimation ofXp for heavy tails. Since the classical semi-parametric estimators exhibit a reasonably high bias for low thresholds, we shall deal with bias reduction techniques, trying to improve their performance.