Estimating of the Proportional Hazard Premium for Heavy-Tailed Claim Amounts with the Pot Method

Abstract

In this paper we propose a new estimator of the proportional hazard premium for heavy-tailed claim amounts, with a help of the peak-over-threshold (POT) method. We establish the asymptotic normality of the new estimator, and its performance is illustrated in a simulation study. Moreover, we compare, in terms of bias and mean squared error, our estimator with the estimator of Necir and Meraghni (2009).