Risk minimization for an insurer with investment and reinsurance via g-expectation

This paper is devoted to the study of a risk-based optimal investment and proportional reinsurance problem. The surplus process of the insurer and the risky asset process in the financial market are assumed to be general jump-diffusion processes. We use a convex risk measure generated by g-expectation to describe the risk of the terminal wealth with investment and reinsurance. Under the aim of minimizing the risk, the problem is solved by using techniques of stochastic maximum principles. Two interesting special cases are studied and the explicit expressions for optimal strategies and corresponding minimal risks are derived.