SummaryThis 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.

In this paper, we consider the infinite horizon nonlinear optimal control of forward–backward stochastic system governed by Teugels martingales associated with Lévy processes and one dimensional independent Brownian motion. Our aim is to establish the sufficient and necessary conditions for optimality of the above stochastic system under the convexity assumptions. Finally an application is given to illustrate the problem of optimal control of stochastic system.

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