Applying the Proportional Hazard Premium Calculation Principle

In this paper we discuss the application of the proportional hazard premium calculation principle. In Section 2 we propose a method to calculate the proportional hazard premium of a compound risk when the severity distribution is subexponential. In Section 3 we use the empirical distribution to calculate the premium when the proportional hazard principle is applied, which leads to a systematic underestimation of the premium. After studying the bias of the premium calculated using this non-parametric approach we take advantage of the bootstrap technique with subsampling to reduce it.