Optimal time-consistent mean-variance reinsurance investment strategies for insurers under the Heston-Hawkes SV model

In this paper, we consider an optimal time-consistent reinsurance-investment strategy problem for an insurer whose surplus process is governed by a diffusion model. To transfer some of the risk associated with insurance claims, an insurer is allowed to purchase proportional reinsurance. In addition, an insurer invests its surplus in a simplified financial market consisting of a risk-free asset and a risky asset, whose price process follows the Heston-Hawkes SV model, which is an extension of the classical Heston model. We derive the explicit expressions of the time-consistent reinsurance-investments strategies under two conditions: for the investment-reinsurance case and for investment-only, and the corresponding value function was also provided. Finally, we show numerically how variations in certain model parameters affect the optimal reinsurance-investment strategy.