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The Steepest Descent Method for Forward-Backward SDEs

Cvitanić, Jakša and Zhang, Jianfeng (2005) The Steepest Descent Method for Forward-Backward SDEs. Electronic Journal of Probability, 10 (45). pp. 1468-1495. ISSN 1083-6489. http://resolver.caltech.edu/CaltechAUTHORS:CVIejp05

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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.


Item Type:Article
Additional Information:Submitted to EJP on July 26, 2005. Final version accepted on December 1, 2005. Published on: December 19, 2005. We are very grateful to the anonymous referee for his/her careful reading of the manuscript and many very helpful suggestions.
Subject Keywords:Forward-Backward SDEs, quasilinear PDEs, stochastic control, steepest decent method, Monte-Carlo method, rate of convergence
Record Number:CaltechAUTHORS:CVIejp05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CVIejp05
Alternative URL:http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1556&layout=abstract
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1253
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:06 Jan 2006
Last Modified:26 Dec 2012 08:43

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