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Volume 10, Issue 2
Deferred Correction Methods for Forward Backward Stochastic Differential Equations

Tao Tang, Weidong Zhao & Tao Zhou

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 222-242.

Published online: 2017-10

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The deferred correction (DC) method is a classical method for solving ordinary differential equations; one of its key features is to iteratively use lower order numerical methods so that high-order numerical scheme can be obtained. The main advantage of the DC approach is its simplicity and robustness. In this paper, the DC idea will be adopted to solve forward backward stochastic differential equations (FBSDEs) which have practical importance in many applications. Noted that it is difficult to design high-order and relatively "clean" numerical schemes for FBSDEs due to the involvement of randomness and the coupling of the FSDEs and BSDEs. This paper will describe how to use the simplest Euler method in each DC step–leading to simple computational complexity–to achievehigh order rate of convergence.

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@Article{NMTMA-10-222, author = {Tao Tang, Weidong Zhao and Tao Zhou}, title = {Deferred Correction Methods for Forward Backward Stochastic Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {2}, pages = {222--242}, abstract = {

The deferred correction (DC) method is a classical method for solving ordinary differential equations; one of its key features is to iteratively use lower order numerical methods so that high-order numerical scheme can be obtained. The main advantage of the DC approach is its simplicity and robustness. In this paper, the DC idea will be adopted to solve forward backward stochastic differential equations (FBSDEs) which have practical importance in many applications. Noted that it is difficult to design high-order and relatively "clean" numerical schemes for FBSDEs due to the involvement of randomness and the coupling of the FSDEs and BSDEs. This paper will describe how to use the simplest Euler method in each DC step–leading to simple computational complexity–to achievehigh order rate of convergence.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.s02}, url = {http://global-sci.org/intro/article_detail/nmtma/12344.html} }
TY - JOUR T1 - Deferred Correction Methods for Forward Backward Stochastic Differential Equations AU - Tao Tang, Weidong Zhao & Tao Zhou JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 222 EP - 242 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.s02 UR - https://global-sci.org/intro/article_detail/nmtma/12344.html KW - AB -

The deferred correction (DC) method is a classical method for solving ordinary differential equations; one of its key features is to iteratively use lower order numerical methods so that high-order numerical scheme can be obtained. The main advantage of the DC approach is its simplicity and robustness. In this paper, the DC idea will be adopted to solve forward backward stochastic differential equations (FBSDEs) which have practical importance in many applications. Noted that it is difficult to design high-order and relatively "clean" numerical schemes for FBSDEs due to the involvement of randomness and the coupling of the FSDEs and BSDEs. This paper will describe how to use the simplest Euler method in each DC step–leading to simple computational complexity–to achievehigh order rate of convergence.

Tao Tang, Weidong Zhao and Tao Zhou. (2017). Deferred Correction Methods for Forward Backward Stochastic Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 10 (2). 222-242. doi:10.4208/nmtma.2017.s02
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