Reduced Bias Estimation of the Reinsurance Premium of Loss Distribution

In this paper we propose a new asymptotically normal estimator of the reinsurance premium for the losses distribution. Our estimator is based on the reduced bias of the extreme quantile and the index of an heavy-tailed distribution. Moreover, we illustrate the behaviour of the proposed estimator and give a comparison between this estimator and the classical semi parametric estimator proposed by Necir et al. (2007) in terms of the bias and the root mean squared error (rmse).