Bulletin of the
Korean Mathematical Society BKMS

This paper analyzes a robust optimal reinsurance and investment strategy for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and insists on seeking robust optimal strategies. The AAI's surplus process is assumed to follow a jump-diffusion model, and he is allowed to purchase proportional reinsurance or acquire new business, meanwhile invest his surplus in a risk-free asset and a risky-asset, whose price is described by an Ornstein-Uhlenbeck process. Under the criterion for maximizing the expected exponential utility of terminal wealth, robust optimal strategy and value function are derived by applying the stochastic dynamic programming approach. Serval numerical examples are given to illustrate the impact of model parameters on the robust optimal strategies and the loss utility function from ignoring the model uncertainty.

Keywords: robust optimal control, jump-diffusion process, Ornstein-Uhlenbeck process, Hamilton-Jacobi-Bellman-Isaacs equation

MSC numbers: 91B30, 93E20

Supported by: This work was supported by National Natural Science Foundation of China (11771320, 11871050) and Natural Science Foundation of Shandong Province (ZR2019MA031)