Abstract

The ruin probability, the joint density function of the surplus immediately prior to ruin, the deficit at ruin, and the time to ruin and the expected discounted penalty function for the classical as well as for the diffusion risk model have been studied by many authors. We consider a sequence of risk processes, which converges weakly to the standard Wiener process when, for instance, the number of policies in a large insurance portfolio goes to infinity, and is added to the classical risk process. The resultant process is a diffusion perturbed classical risk model. We study this model and obtained the ruin probabilities, the joint density function of the surplus immediately prior to ruin, the deficit at ruin, the time to ruin and the expected discounted penalty function for the diffusion risk model by the weak convergence. In other words, we show that these quantities converge weekly to the corresponding quantities of the diffusion risk model for large number of policies. Numerical illustrations of the expected discounted penalty function and ruin probabilities are also presented.