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Linear-Quadratic Pareto Cooperative Game for Mean-Field Backward Stochastic System

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Abstract

This paper focuses on a Pareto cooperative differential game with a linear mean-field backward stochastic system and a quadratic form cost functional. Based on a weighted sum optimality method, the Pareto game is equivalently converted to an optimal control problem. In the first place, the feedback form of Pareto optimal strategy is derived by virtue of decoupling technology, which is represented by four Riccati equations, a mean-field forward stochastic differential equation (MF-FSDE), and a mean-field backward stochastic differential equation (MF-BSDE). In addition, the corresponding Pareto optimal solution is further obtained. Finally, the author solves a problem in mathematical finance to illustrate the application of the theoretical results.

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Acknowledgements

The author would like to thank Professor Guangchen Wang for many suggestions for improving the quality of the work.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Yu Wang

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  1. Yu Wang
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Corresponding author

Correspondence to Yu Wang.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Key R&D Program of China under Grant No. 2022YFA1006103, the National Natural Science Foundation of China under Grant Nos. 61821004, 61925306, and 11831010, and the Natural Science Foundation of Shandong Province under Grant Nos. ZR2019ZD42 and ZR2020ZD24.

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Cite this article

Wang, Y. Linear-Quadratic Pareto Cooperative Game for Mean-Field Backward Stochastic System. J Syst Sci Complex 37, 947–964 (2024). https://doi.org/10.1007/s11424-024-3091-6

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  • DOI: https://doi.org/10.1007/s11424-024-3091-6

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