@article{EJP295,
author = {Jaksa Cvitanic and Jianfeng Zhang},
title = {The Steepest Descent Method for Forward-Backward SDEs},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {10},
year = {2005},
keywords = {},
abstract = {This paper aims to open a door to Monte-Carlo methods for numerically solving Forward-Backward SDEs, without computing over all Cartesian grids as usually done in the literature. We transform the FBSDE to a control problem and propose the steepest descent method to solve the latter one. We show that the original (coupled) FBSDE can be approximated by {it decoupled} FBSDEs, which further comes down to computing a sequence of conditional expectations. The rate of convergence is obtained, and the key to its proof is a new well-posedness result for FBSDEs. However, the approximating decoupled FBSDEs are non-Markovian. Some Markovian type of modification is needed in order to make the algorithm efficiently implementable.},
pages = {no. 45, 1468-1495},
issn = {1083-6489},
doi = {10.1214/EJP.v10-295},
url = {http://ejp.ejpecp.org/article/view/295}}