We consider a time-consistent mean–variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an optimal strategy as solution of a system of partial integro-differential equations (PIDEs), a so called extended Hamilton–Jacobi–Bellman (HJB) system. We prove that the equilibrium is necessarily a solution of the extended HJB system. Under certain conditions we obtain an explicit solution to the extended HJB system and provide the optimal trading strategies in closed-form. A simulation shows that the previously found strategies yield payoffs whose expectations and variances are robust regarding the distribution of jump sizes of the stock. The same phenomenon is observed when the variance is correctly estimated, but erroneously ascribed to the diffusion components solely. Further, we show that differences in the insurance horizon and the time to maturity of a longevity asset do not add to the variance of the terminal wealth.

我们考虑保险公司的时间一致均值方差投资组合选择问题，并允许纳入基础（死亡率）风险。最优解由纳什子博弈完美均衡确定。我们将最优策略描述为偏积分微分方程 (PIDE) 系统的解，即所谓的扩展 Hamilton-Jacobi-Bellman (HJB) 系统。我们证明了均衡必然是扩展 HJB 系统的解。在特定条件下，我们获得扩展 HJB 系统的显式解，并以封闭形式提供最佳交易策略。模拟表明，先前发现的策略会产生收益，其预期和方差对于股票跳跃大小的分布是稳健的。当方差被正确估计时，观察到相同的现象，但错误地仅归因于扩散成分。此外，我们表明，保险期限和长寿资产到期时间的差异不会增加终端财富的差异。