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

Tianjiao Hua () and Peng Luo ()
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Tianjiao Hua: Shanghai Jiao Tong University
Peng Luo: Shanghai Jiao Tong University

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-29

Abstract: 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.

Keywords: Mean-field-type FBSDE; Global solution; Decoupling field; Master equation; 60H30; 49N80 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01375-9

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