Partial information optimal control of mean-field forward–backward stochastic system driven by Teugels martingales with applications

In this paper, we study the partial information optimal control of mean-field forward–backward stochastic systems, driven by orthogonal Teugels martingales associated with some Lévy processes heaving moments of all orders, and an independent Brownian motion. We establish necessary and sufficient conditions of optimality by applying convex variation method and duality techniques. As an application, we study a partial information mean–variance portfolio selection problem, driven by Teugels martingales associated with Gamma process, where the explicit optimal portfolio strategy is derived in feedback form.