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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 | | Abstract: | In 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 | | Services: | Forum | Review | PDF | Favorites | |
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