Surplus Prior to Ruin and the Deficit at Ruin in the Perturbed Classical Risk Process

The purpose of this article is to consider the classical risk model that is perturbed by a wiener process. The article derives explicit formulas for the joint and marginal probability density functions of the surplus prior to ruin and the deficit at ruin and also probability density function of claim size that cause ruin. Request for this research is because we don’t find a correct answer for probability of ruin when we don’t consider some factor in reality insurance data such as interest, inflation, etc. The diffusion term expresses an additional uncertainty of the aggregate claims; an alternative interpretation is that it adds an uncertainty to the premium income.But the most important purpose in this research is finding matrix algebra forms for probability of ruin, probability density function of surplus immediately prior ruin and at ruin and size of claims that causing ruin, then we apply these matrix algebra forms for writing separate computer programs. These programs give us amount of ruin probability and draw probability density functions diagrams of surplus prior ruin and at ruin, and size of claims that causing ruin.