Statistical estimate of the proportional hazard premium of loss under random censoring

Many insurance premium principles are defined and various estimation procedures introduced in the literature. In this paper, we focus on the estimation of the excess-of-loss reinsurance premium when the risks are randomly right-censored. The asymptotic normality of the proposed estimator is established under suitable conditions and its performance evaluated through sets of simulated data.Comment: arXiv admin note: text overlap with arXiv:1507.03178, arXiv:1302.166

Distortion risk measures for sums of dependent losses

We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the sum and the dependence structure of risks, represented by copulas. Our goal is to propose risk measures that take into account the fluctuations of losses and possible correlations between risk components.Comment: Accepted 25 October 2010, Journal Afrika Statistika Vol. 5, N9, 2010, page 260--26