The maximum principle for optimal control of mean-field FBSDE driving by Teugels martingales with terminal state constraints

This article studies the problem of optimal control with state constraints for mean-field type stochastic systems, which is governed by a fully coupled forward-backward stochastic differential equation with Teugels martingales. In this system, the coefficients contain not only the state processes but also its expectation value, and the cost function is of mean-field type as well. We use an equivalent backward formulation to deal with the terminal state constraint, and then we obtain a stochastic maximum principle by Ekeland's variational principle. In addition, we discuss a stochastic linear-quadratic control problem with state constraints.