Alpha-robust investment-reinsurance strategy for a mean-variance insurer with delay

Abstract: In this paper, a robust optimal reinsurance-investment problem with delay is studied under the $\alpha$-maxmin mean-variance criterion. The surplus process of an insurance company approximates Brownian motion with drift. The financial market consists of a risk-free asset and a risky asset that obeys geometric Brownian motion. Using the principle of dynamic programming and Hamilton-Jacobin-Bellman (HJB) equation, the specific expression of optimal strategy and the explicit solution of the corresponding HJB equation are obtained. In addition, a verification theorem is provided to ensure that the value function is indeed the solution of the HJB equation. Finally, some numerical examples and graphs are given to illustrate the results, and the influence of some important parameters in the model on the optimal strategy is discussed.