American Institute of Mathematical Sciences

July  2006, 6(4): 927-940. doi: 10.3934/dcdsb.2006.6.927

The wellposedness of FBSDEs

 1 USC Mathematics Department, 3620 Vermont Ave, KAP 108, Los Angeles, CA 90089, United States

Received  January 2005 Revised  September 2005 Published  April 2006

In this paper we investigate the wellposedness of a class of Forward-Backward SDEs. Compared to the existing methods in the literature, our result has the following features: (i) arbitrary time duration; (ii) random coefficients; (iii) (possibly) degenerate forward diffusion; and (iv) no monotonicity condition. As a trade off, we impose some assumptions on the derivatives of the coefficients. A comparison theorem is also proved under the same conditions. This work is motivated by studying numerical methods for FBSDEs.
Citation: Jianfeng Zhang. The wellposedness of FBSDEs. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 927-940. doi: 10.3934/dcdsb.2006.6.927
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