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Well-Posedness for a Class of Mean-Field-Type Forward-Backward Stochastic Differential Equations and Classical Solutions of Related Master Equations

Author

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  • Tianjiao Hua

    (Shanghai Jiao Tong University)

  • Peng Luo

    (Shanghai Jiao Tong University)

Abstract

In this paper, we study a class of mean-field-type forward-backward stochastic differential equations. We propose a class of monotonicity conditions, under which we show the uniformly Lipschitz continuity of the decoupling field and obtain the existence and uniqueness of solution. We further provide a representation result for the solution and the decoupling field. Finally, we obtain the regularity of the decoupling field and establish global well-posedness of classical solutions to related master equations.

Suggested Citation

  • Tianjiao Hua & Peng Luo, 2025. "Well-Posedness for a Class of Mean-Field-Type Forward-Backward Stochastic Differential Equations and Classical Solutions of Related Master Equations," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-29, March.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01375-9
    DOI: 10.1007/s10959-024-01375-9
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    References listed on IDEAS

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    1. 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.
    2. 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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