ON THE TIME VALUE OF RUIN IN THE DISCRETE TIME RISK MODEL

Using an approach similar to that of Gerber and Shiu (1998), a recursive formula is given for the expected discounted penalty due at ruin, in the discrete time risk model. With it the joint distribution of three random variables is obtained; time to ruin, the surplus just before ruin and the deficit at ruin. The time to ruin is analyzed through its probability generating function (p.g.f.). The joint distribution for the compound binomial model is derived in Cheng et al. (2000) using martingale techniques and a duality argument. Here we find a recursive formula for the p.g.f. of ruin time T; the discounted moments of the deficit at ruin and the surplus just before ruin. A detailed discussion is given in the case u = 0 and when the claim size in a unit time is geometrically distributed.