Variational principle for stochastic singular control of mean-field Levy-forward-backward system driven by orthogonal Teugels martingales with application

We consider stochastic singular control for mean-field forward-backward stochastic differential equations, driven by orthogonal Teugels martingales associated with some Levy processes having moments of all orders and an independent Brownian motion. Under partial information, necessary and sufficient conditions for optimality in the form of maximum principle for this mean-field system are established by means of convex variation methods and duality techniques. As an illustration, this paper studies a partial information mean-variance portfolio selection problem driven by orthogonal Teugels martingales associated with gamma process as Levy process of bounded variation.