A Mean-Field Game for a Forward-Backward Stochastic System with Partial Observation and Common Noise

This paper considers a linear-quadratic (LQ) mean-field game governed by a forward-backward stochastic system with partial observation and common noise, where a coupling structure enters state equations, cost functionals and observation equations. Firstly, to reduce the complexity of solving the mean-field game, a limiting control problem is introduced. By virtue of the decomposition approach, an admissible control set is proposed. Applying a filter technique and dimensional-expansion technique, a decentralized control strategy and a consistency condition system are derived, and the related solvability is also addressed. Secondly, we discuss an approximate Nash equilibrium property of the decentralized control strategy. Finally, we work out a financial problem with some numerical simulations.