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Forward–backward stochastic differential equations with monotone functionals and mean field games with common noise

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  • Ahuja, Saran
  • Ren, Weiluo
  • Yang, Tzu-Wei

Abstract

We consider a system of forward–backward stochastic differential equations (FBSDEs) with monotone functionals. We show that such a system is well-posed by the method of continuation similarly to Peng and Wu (1999) for classical FBSDEs. As applications, we prove the well-posedness result for a mean field FBSDE with conditional law and show the existence of a decoupling function. Lastly, we show that mean field games with common noise are uniquely solvable under a linear-convex setting and weak-monotone cost functions and prove that the optimal control is in a feedback form depending only on the current state and conditional law.

Suggested Citation

  • Ahuja, Saran & Ren, Weiluo & Yang, Tzu-Wei, 2019. "Forward–backward stochastic differential equations with monotone functionals and mean field games with common noise," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3859-3892.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:3859-3892
    DOI: 10.1016/j.spa.2018.11.005
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    References listed on IDEAS

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    1. Alain Bensoussan & Jens Frehse & Phillip Yam, 2014. "The Master Equation in Mean Field Theory," Papers 1404.4150, arXiv.org, revised Nov 2014.
    2. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    3. Rene Carmona & Jean-Pierre Fouque & Li-Hsien Sun, 2013. "Mean Field Games and Systemic Risk," Papers 1308.2172, arXiv.org.
    4. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    5. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    6. Bensoussan, A. & Yam, S.C.P. & Zhang, Z., 2015. "Well-posedness of mean-field type forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3327-3354.
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    Cited by:

    1. Dianetti, Jodi, 2023. "Strong Solutions to Submodular Mean Field Games with Common Noise and Related McKean-Vlasov FBSDES," Center for Mathematical Economics Working Papers 674, Center for Mathematical Economics, Bielefeld University.
    2. Dianetti, Jodi & Riedel, Frank & Stanza, Lorenzo, 2024. "Optimal consumption and Investment under Relative Performance Criteria with Epstein-Zin Utility," Center for Mathematical Economics Working Papers 685, Center for Mathematical Economics, Bielefeld University.
    3. Tianyang Nie & Falei Wang & Zhiyong Yu, 2022. "Maximum Principle for General Partial Information Nonzero Sum Stochastic Differential Games and Applications," Dynamic Games and Applications, Springer, vol. 12(2), pages 608-631, June.

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