ON THE DISTRIBUTION OF THE SURPLUS PRIOR TO RUIN

The distribution of the surplus immediately prior to ruin in the classical compound Poisson risk model was considered in a paper by Dufresne and Gerber (1988). The main purpose of this paper is to present a simple method for finding the distribution function and the density function of this surplus. We show that explicit solutions for these functions can be found when we know the probability and severity of ruin, denoted G(u, y). We also derive an algorithm which can be used to give approximate values of the distribution function when explicit solutions cannot be found. We also briefly consider the joint density of the surplus immediately prior to ruin and the deficit at the time of ruin.