Robust Optimal Reinsurance-Investment for $\Alpha$-Maxmin Mean-Variance Utility Under Heston's Sv Model

Most literatures about robust optimal reinsurance-investment problem aim to maximum the value function under the worst-case scenario, but some insurers are optimistic, so it is more reasonable to consider a more smooth criterion named $\alpha$-maxmin criterion which seek a balance between the worst-case scenario and best-case scenario. Furthermore, the past performance of insurance company will heavily impact the reinsurance-investment strategy of insurer, by introducing the capital flow related to the historical performance of the insurer, the wealth process can be described by stochastic delay differential equation. In this paper, we consider the robust optimal reinsurance-investment strategy for an $\alpha$-maxmin mean-variance insurer with delay under Heston's stochastic volatility stock model, the verification theorem is given and the closed-form solutions of value function and optimal strategies are obtained, respectively. In the part of numerical analysis, we illustrate the influence of some important parameters on the optimal strategies