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25 September 2022
 
  » arxiv » 1110.4658

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On Wellposedness of Forward-Backward SDEs --- A Unified Approach
Jin Ma ; Zhen Wu ; Detao Zhang ; Jianfeng Zhang ;
Date 21 Oct 2011
AbstractIn this paper we study the wellposedness 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 overcome some fundamental difficulties that have been longstanding problems for non-Markovian FBSDEs. Our main devices are a {it decoupling random field} and its associated {it characteristic BSDE}, a backward stochastic Riccati-type equation with superlinear growth in both components $Y$ and $Z$. We establish various sufficient conditions under which the characteristic BSDE is wellposed, which leads to the existence of the decoupling random field, and ultimately to the solvability of the original FBSDE. We show that all existing frameworks could be analyzed using our new criteria.
Source arXiv, 1110.4658
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