The Maximum Principle with Terminal State Constraints for Optimal
Control of Mean-Field FBSDE Driving by Teugels Martingales
Abstract
This paper studies the problem of optimal control with state constraints
for mean-field type stochastic systems, which is governed by fully
coupled forward-backward stochastic differential equations(FBSDE) with
Teugels martingales. In this system, the coefficients contain not only
the state processes but also its marginal distribution, 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 LQ control problem with
state constraints.