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Volume 11 Issue 3
Mar.  2024

IEEE/CAA Journal of Automatica Sinica

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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
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

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

doi: 10.1109/JAS.2023.124047
Funds:  This work was supported by the National Key Research and Development Program of China (2022YFA1006103, 2023YFA1009203), the National Natural Science Foundation of China (61925306, 61821004, 11831010, 61977043, 12001320), the Natural Science Foundation of Shandong Province (ZR2019ZD42, ZR2020ZD24), the Taishan Scholars Young Program of Shandong (TSQN202211032), and the Young Scholars Program of Shandong University
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  • 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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    Highlights

    • The large-population system is governed by an FBSDE with partial observation, which plays a vital role in both theoretical research and practical application
    • By virtue of optimal Filter technique, decomposition technique and dimensional-expansion technique, we get a decentralized control strategy, which is an approximate Nash equi- librium of the mean-field game
    • This work significantly improves the description and resolution of mean-field game with partial observation. In addition, this work compensates for the deficiencies and aws,and the results obtained are more elaborate and rigorous than some existing works

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