The Aggregate Claims Process

Abstract

In the present chapter we introduce and study the aggregate claims process. We first extend the model considered so far (Section 5.1) and then establish some general results on compound distributions (Section 5.2). It turns out that aggregate claims distributions can be determined explicitly only in a few exceptional cases. However, the most important claim number distributions can be characterized by a simple recursion formula (Section 5.3) and admit the recursive computation of aggregate claims distributions and their moments when the claim size distribution is discrete (Section 5.4).