This paper investigates the asset-liability management problem for an ordinary robust insurance system between a reinsurer and an insurer under the Heston model with delay. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium and invest its wealth in a financial market that contains a risk-free asset and a risky asset whose price process is described by the Heston model. The insurer, as the follower of the Stackelberg game, can purchase proportional reinsurance from the reinsurer and invest in the same financial market. Under the consideration of the performance-related capital inflow/outflow, the wealth processes of the insurer and reinsurer are modeled by stochastic differential delay equations (SDDEs). This paper aims to find the equilibrium strategies for the reinsurer and insurer by maximizing the expected utility of the player’s terminal wealth with delay under the worst-case scenario of the alternative measures. By using the idea of backward induction and dynamic programming approach, the explicit expressions of the robust equilibrium strategies and value functions are derived. Finally, some numerical examples and sensitivity analysis to illustrate the effects of model parameters on the robust optimal reinsurance and investment strategies are performed.

本文研究了在Heston模型下，时滞的再保险人与保险人之间的普通健壮保险系统的资产负债管理问题。作为Stackelberg游戏的领导者，再保险公司可以对再保险保费进行定价，并将其财富投资到包含无风险资产和风险资产的金融市场中，该资产的定价过程由Heston模型描述。作为Stackelberg游戏的追随者，该保险公司可以从该再保险公司购买比例再保险，并在同一金融市场上进行投资。在考虑与绩效相关的资本流入/流出时，用随机微分延迟方程（SDDE）对保险人和再保险人的财富过程进行建模。本文旨在通过在替代措施的最坏情况下最大程度地延误参与者的终端财富的预期效用来找到再保险人和保险人的均衡策略。通过使用反向归纳和动态规划方法的思想，得出了鲁棒均衡策略和值函数的显式表达式。最后，进行了一些数值算例和敏感性分析，以说明模型参数对稳健的最优再保险和投资策略的影响。