Research on the collective risk stochastic process

Abstract

Abstract The subject of collective risk has been extensively studied by Scandinavian actuaries. Many articles in this journal and elsewhere have treated the theory and applications of the subject. The purpose of this article is to use these existing works in applying a paper of G. Baxter and M. Donsker [4] to both the ruin and distribution branches of risk theory. In section II, the risk process is briefly described. In section III, a general theorem based on [4] is proved. This yields expressions for the ruin and distribution functions. Section IV discusses these expressions, and gives three examples, including two tables.