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

Abstract

Many insurance premium principles are dened and various estimation procedures introduced in the literature. In this paper, we focus on the estimation of the excessof- 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.

Keywords: Heavy tails; Hill estimator; Kaplan-Meier estimator; Proportional hazard premium; Random censoring; Reinsurance treaty