The wellposedness of FBSDEs

Jianfeng Zhang

doi:10.3934/dcdsb.2006.6.927

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2006, Volume 6, Issue 4: 927-940. Doi: 10.3934/dcdsb.2006.6.927

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The wellposedness of FBSDEs

Jianfeng Zhang^1,

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

Received: December 31, 2004

Revised: August 31, 2005

Published: June 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 60H10.

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