Ruin probabilities in a finite-horizon risk model with investment and reinsurance

摘要

A finite horizon insurance model is studied where the risk/reserveprocess can be controlled by reinsurance and investment in the financialmarket. Obtaining explicit optimal solutions for the minimizingruin probability problem is a difficult task. Therefore, we consider analternative method commonly used in ruin theory, which consists inderiving inequalities that can be used to obtain upper bounds for theruin probabilities and then choose the control to minimize the bound.We finally specialize our results to the particular, but relevant, case ofexponentially distributed claims and compare for this case our boundswith the classical Lundberg bound.