IEEE/CAA Journal of Automatica Sinica
Citation: | P. Huang, G. Wang, S. Wang, and H. Xiao, “A mean-field game for a forward-backward stochastic system with partial observation and common noise,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 3, pp. 746–759, Mar. 2024. doi: 10.1109/JAS.2023.124047 |
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.
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