Optimal investment, consumption and proportional reinsurance under model uncertainty

This paper considers the optimal investment, consumption and proportional reinsurance strategies for an insurer under model uncertainty. The surplus process of the insurer before investment and consumption is assumed to be a general jump-diffusion process. The financial market consists of one risk-free asset and one risky asset whose price process is also a general jump-diffusion process. We transform the problem equivalently into a two-person zero-sum forward-backward stochastic differential game driven by two-dimensional Lévy noises. The maximum principles for a general form of this game are established to solve our problem. Some special interesting cases are studied by using Malliavin calculus so as to give explicit expressions of the optimal strategies.