Abstract
In this paper, we study the well-posedness of the Forward–Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the literature, and to address some fundamental longstanding problems for non-Markovian FBSDEs. An important device is a decoupling random field that is regular (uniformly Lipschitz in its spatial variable). We show that the regulariy of such decoupling field is closely related to the bounded solution to an associated characteristic BSDE, a backward stochastic Riccati-type equation with superlinear growth in both components
Citation
Jin Ma. Zhen Wu. Detao Zhang. Jianfeng Zhang. "On well-posedness of forward–backward SDEs—A unified approach." Ann. Appl. Probab. 25 (4) 2168 - 2214, August 2015. https://doi.org/10.1214/14-AAP1046
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