MODELS FOR THE DISTRIBUTION OF AGGREGATE CLAIMS IN RISK THEORY
Harry H. Panjer, Gordon E. WlLLMOT · 1984
This paper considers the distribution of aggregate claims of an insurer. The general form of the distribution is considered initially, and, after a few mild restrictions are imposed, it is characterized as being a compound distribution. Various models for the aggregate claims as well as the number-of-claims distribution are presented. Special emphasis is placed on characterizing the aggregate claims random variable as Compound Poisson, using the concepts of infinite divisibility and Bayesian uncertainty models. Results from stochastic process theory are applied to the modeling of the risk process faced by an insurer. The paper further provides a comprehensive review of related results that have appeared in the actuarial and statistical literature.