In this paper, we study the optimal time-consistent reinsurance-investment problem for a risk model with the thinning-dependence structure. The insurer’s wealth process is described by a jump-diffusion risk model with two dependent classes of insurance business. We assume that the insurer is allowed to purchase per-loss reinsurance and invest its surplus in a financial market consisting of a risk-free asset and a risky asset. Also, the performance-related capital inflow or outflow feature is introduced, and the wealth process is modeled by a stochastic delay differential equation. Under the time-inconsistent mean-variance criterion, we derive the explicit optimal reinsurance-investment strategy and value function under the expected value premium principle as well as the variance premium principle by solving the extended Hamilton–Jacobi–Bellman (HJB) delay system. In particular, we prove the existence and uniqueness of the optimal strategy under the expected value premium principle. Finally, some numerical examples are provided to illustrate the influence of model parameters on the optimal strategy.

在本文中，我们研究了具有稀疏依赖结构的风险模型的最优时间一致再保险投资问题。保险公司的财富过程由具有两个相关保险业务类别的跳跃扩散风险模型来描述。我们假设保险公司被允许购买按损失再保险，并将其盈余投资于由无风险资产和风险资产组成的金融市场。此外，还引入了与绩效相关的资本流入或流出特征，并通过随机时滞微分方程对财富过程进行了建模。在时间不一致均值方差准则下，通过求解扩展的Hamilton-Jacobi-Bellman (HJB)时滞系统，推导出期望价值保费原理和方差保费原理下的显式最优再保险投资策略和价值函数。特别是，我们证明了期望价值溢价原则下最优策略的存在性和唯一性。最后，提供了一些数值例子来说明模型参数对最优策略的影响。