Collective risk model in heterogeneous portfolios of policies

Abstract

The total amount of claims in a particular time period, in actuarial literature named as collective risk, is a quantity of fundamental importance to the proper management of an insurance company. The article aimed to present the possibility and procedure to approximate the collective risk model in a heterogeneous portfolio of policies. The key assumption in all models for aggregate claim amount is that the occurrence of a claim and the amount of a claim can be studied separately. We will show that mixture distributions are convenient as the probability models for claim numbers and for claim amounts in heterogeneous portfolios of policies. We have derived that the negative binomial distribution can be used as a model for claim frequency and the Pareto distribution as a loss distribution model when the portfolios of policies are not homogeneous. The concept of mixture distributions is an important one in insurance, since insurance companies generally deal with heterogeneous risks. The motor compulsory third party liability insurance is an important branch of non-life insurance in many countries; therefore application of the theoretical results is performed on data from this field.