Risk processes connected with the compound poisson process

Abstract

A portfolio of casualty insurances is usually very heterogeneous due to the wide spread of the individual risks also in case the policies are grouped according to risk classes. Stochastic models assuming identical risks for all policies in the risk class—e.g, the simple Poisson distribution—are not generally applicable to such a portfolio. For this reason it has been tried to consider the individual risk as a random variable governed by a given but unknown distribution function U(v) which is called the structure function of the individual risk process. This model of probability distributions can be led back to the Lens urn scheme.