Recursive calculation of the probability and severity of ruin

In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. © 1989.