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Volume 9, Issue 2
A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations

Weidong Zhao, Wei Zhang & Lili Ju

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 262-288.

Published online: 2016-09

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  • Abstract

Upon a set of backward orthogonal polynomials, we propose a novel multi-step numerical scheme for solving the decoupled forward-backward stochastic differential equations (FBSDEs). Under Lipschtiz conditions on the coefficients of the FBSDEs, we first get a general error estimate result which implies zero-stability of the proposed scheme, and then we further prove that the convergence rate of the scheme can be of high order for Markovian FBSDEs. Some numerical experiments are presented to demonstrate the accuracy of the proposed multi-step scheme and to numerically verify the theoretical results.

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@Article{NMTMA-9-262, author = {}, title = {A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {2}, pages = {262--288}, abstract = {

Upon a set of backward orthogonal polynomials, we propose a novel multi-step numerical scheme for solving the decoupled forward-backward stochastic differential equations (FBSDEs). Under Lipschtiz conditions on the coefficients of the FBSDEs, we first get a general error estimate result which implies zero-stability of the proposed scheme, and then we further prove that the convergence rate of the scheme can be of high order for Markovian FBSDEs. Some numerical experiments are presented to demonstrate the accuracy of the proposed multi-step scheme and to numerically verify the theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.m1421}, url = {http://global-sci.org/intro/article_detail/nmtma/12377.html} }
TY - JOUR T1 - A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 262 EP - 288 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.m1421 UR - https://global-sci.org/intro/article_detail/nmtma/12377.html KW - AB -

Upon a set of backward orthogonal polynomials, we propose a novel multi-step numerical scheme for solving the decoupled forward-backward stochastic differential equations (FBSDEs). Under Lipschtiz conditions on the coefficients of the FBSDEs, we first get a general error estimate result which implies zero-stability of the proposed scheme, and then we further prove that the convergence rate of the scheme can be of high order for Markovian FBSDEs. Some numerical experiments are presented to demonstrate the accuracy of the proposed multi-step scheme and to numerically verify the theoretical results.

Weidong Zhao, Wei Zhang & Lili Ju. (2020). A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 9 (2). 262-288. doi:10.4208/nmtma.2016.m1421
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