SHARP CONDITIONS FOR CERTAIN RUIN IN A RISK PROCESS WITH STOCHASTIC RETURN ON INVESTMENTS

We consider a classical risk process compounded by another independent process. Both of these component processes are assumed to be Levy pro cesses. Sharp conditions are given on the parameters of these two comp onents to ensure when ruin is certain, and also when the time of ruin is of exponential type. It is shown that under some weak conditions, t hese problems depend only on the compounding process. When ruin is not certain, it is shown in Paulsen (1993) that the ruin probability depe nds on the distribution function of a certain present value, and an in tegro-differential equation for the characteristic function is found t here in the special case when the two component Levy processes have on ly a finite number of jumps on any finite time interval. We generalize this equation to the present case. (C) 1998 Elsevier Science B.V. All rights reserved.