Upper bound for ruin probabilities under optimal investment and proportional reinsurance

In this paper, we consider the optimal investment and reinsurance from an insurer's point of view to maximize the adjustment coefficient. We obtain the explicit expressions for the optimal results in the diffusion approximation (D-A) case as well as in the jump-diffusion (J-D) case. Furthermore, we derive a sharper bound on the ruin probability, from which we conclude that the case with investment is always better than the case without investment. Some numerical examples are presented to show that the ruin probability in the D-A case sometimes underestimates the ruin probability in the J-D case. Copyright (C) 2007 John Wiley & Sons, Ltd.