  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.
