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A mean-field game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

IEEE/CAA Journal of Automatica Sinica 2024年第3期11卷 746-759页

作者： Pengyan Huang Guangchen Wang Shujun Wang Hua Xiao the School of Control Science and Engineering Shandong University the School of Statistics and Mathematics Shandong University of Finance and Economics IEEE the School of Management Shandong University the School of Mathematics and Statistics Shandong University

This paper considers a linear-quadratic(LQ) meanfield 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 ***,to reduce the complexity of solving the meanfield game,a limiting control problem is *** virtue of the decomposition approach,an admissible control set is *** a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also ***,we discuss an approximate Nash equilibrium property of the decentralized control ***,we work out a financial problem with some numerical simulations.

关键词： Decentralized control strategy ϵ-Nash equilibrium forward-backward stochastic system mean-field game partial observation

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Backward-forward linear-quadratic mean-field games with major and minor agents

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Probability, Uncertainty and Quantitative Risk 2016年第1期1卷 278-304页

作者： Jianhui Huang Shujun Wang Zhen Wu Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong kongChina School of Mathematics Shandong University250100 JinanChina

This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states of minor agents are governed by linear forward stochastic differential equations(SDEs).The major agent is dominating as its state enters those of minor *** the other hand,all minor agents are individually negligible but their state-average affects the cost functional of major *** mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized *** first derive the consistency condition via an auxiliary mean-field SDEs and a 3×2 mixed backward-forward stochastic differential equation(BFSDE)***,we discuss the wellposedness of such BFSDE system by virtue of the monotonicity ***,we obtain the decentralized strategies for major and minor agents which are proved to satisfy the-Nash equilibrium property.

关键词： Backward-forward stochastic differential equation(BFSDE) Consistency condition -Nash equilibrium Large-population system Major-minor agent mean-field game

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