Robust optimal investment and reinsurance of an insurer under variance premium principle and default risk

This paper considers a robust optimal investment and reinsurance problem under model ambiguity and default risk for an insurer, who can trade in a saving account, a stock and a defaultable bond and aims to maximize the minimal expected CARA utility. The surplus process of the insurer is assumed to follow the Cramér–Lundberg model. In particular, both the insurance and reinsurance premium are assumed to be calculated via the variance premium principle. By using the dynamic programming approach, we study the pre-default case and post-default case respectively, then closed-form expressions for the optimal strategies and the corresponding value function are derived. Finally, numerical examples are given to illustrate our main results, and we discuss relevant economic insights obtained from these results.