Diffusion approximations for insurance risk processes

Abstract

We consider a risk-reserve process for an insurance company where premium income and the claim sum process are modeled as a renewal reward processes. Moreover, dividends are paid out according to a barrier rule. The aim of the article is to establish a diffusion approximation of this model and to compute ruin probabilities (in finite and in infinite time) and other relevant statistics approximately using the limiting diffusion process. We also demonstrate that, under special circumstances, there exists a stationary distribution for the limiting diffusion.