A Gerber-Shiu Discounted Penalty Function in the Stationary Renewal Risk Process

In this paper, we consider a Gerber-Shiu discounted penalty function in the stationary renewal risk process. By conditioning on the time and the amount of the first claim, we express the Gerber-Shiu discounted penalty function in the stationary renewal risk process in terms of the same function in the ordinary renewal risk model. From this expression, we can obtain some useful relationships about ruin probability, deficit at ruin and the surplus prior to ruin. Finally we illustrate the application of the results with a numerical example.