This article investigates the optimal control problem of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward stochastic system with Lévy processes associated with Teugels martingales over the infinite time horizon. Based on the transversality conditions, assumption of convex control domain, infinite‐horizon version of stochastic maximum principle (Nash equilibrium), and necessary condition for optimality are established. Finally, the Nash equilibrium for the optimization problem in the financial market is considered to illustrate the observed theoretical results.

中文翻译：

---

具有Lévy过程的非零和博弈均值时滞马尔可夫状态切换的最优控制

本文研究了无限时间范围内具有Teugels martingales相关Lévy过程的非零和博弈均值时滞Markov状态切换前向后向随机系统的最优控制问题。基于横向条件，建立了凸控制域的假设，随机最大原理的无限水平版本（纳什均衡）以及最优性的必要条件。最后，考虑了金融市场优化问题的纳什均衡，以说明观察到的理论结果。