Electronic Journal of Probability

The Steepest Descent Method for Forward-Backward SDEs

Jaksa Cvitanic and Jianfeng Zhang

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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 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.

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Electron. J. Probab., Volume 10 (2005), paper no. 45, 1468-1495.

Accepted: 19 December 2005
First available in Project Euclid: 1 June 2016

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Cvitanic, Jaksa; Zhang, Jianfeng. The Steepest Descent Method for Forward-Backward SDEs. Electron. J. Probab. 10 (2005), paper no. 45, 1468--1495. doi:10.1214/EJP.v10-295. https://projecteuclid.org/euclid.ejp/1464816846

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