Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, we show that the proportional hazard rates (PHR) model, which includes some well-known distributions such as exponential, Weibull and Pareto distributions, can be used as the aggregate claim amount distribution. We also present some conditions for the use of exponentiated Weibull distribution as the claim amount distribution. The results established here complete and extend the well-known result of Khaledi and Ahmadi (2008).