Volume 12, Issue 4
One-Step Multi-Derivative Methods for Backward Stochastic Differential Equations

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 1213-1230.

Published online: 2019-06

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• Abstract

This paper deals with numerical solutions of backward stochastic differential equations (BSDEs). For solving BSDEs, a class of third-order one-step multi-derivative methods are derived. Several numerical examples are presented to illustrate the computational effectiveness and high-order accuracy of the methods. To show the advantage of the methods, a comparison with $\theta$-methods is also given.

• Keywords

Backward stochastic differential equations, one-step multi-derivative methods, $\theta$-method, Itô-Taylor expansion, third-order accuracy.

60H35, 65C20, 60H10

cjzhang@hust.edu.cn (Chengjian Zhang)

wdzhao@sdu.edu.cn (Weidong Zhao)

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@Article{NMTMA-12-1213, author = {Zhang , Chengjian and Wu , Jingwen and Zhao , Weidong}, title = {One-Step Multi-Derivative Methods for Backward Stochastic Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {4}, pages = {1213--1230}, abstract = {

This paper deals with numerical solutions of backward stochastic differential equations (BSDEs). For solving BSDEs, a class of third-order one-step multi-derivative methods are derived. Several numerical examples are presented to illustrate the computational effectiveness and high-order accuracy of the methods. To show the advantage of the methods, a comparison with $\theta$-methods is also given.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0122}, url = {http://global-sci.org/intro/article_detail/nmtma/13221.html} }
TY - JOUR T1 - One-Step Multi-Derivative Methods for Backward Stochastic Differential Equations AU - Zhang , Chengjian AU - Wu , Jingwen AU - Zhao , Weidong JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1213 EP - 1230 PY - 2019 DA - 2019/06 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0122 UR - https://global-sci.org/intro/article_detail/nmtma/13221.html KW - Backward stochastic differential equations, one-step multi-derivative methods, $\theta$-method, Itô-Taylor expansion, third-order accuracy. AB -

This paper deals with numerical solutions of backward stochastic differential equations (BSDEs). For solving BSDEs, a class of third-order one-step multi-derivative methods are derived. Several numerical examples are presented to illustrate the computational effectiveness and high-order accuracy of the methods. To show the advantage of the methods, a comparison with $\theta$-methods is also given.

Chengjian Zhang, Jingwen Wu & Weidong Zhao. (2019). One-Step Multi-Derivative Methods for Backward Stochastic Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 12 (4). 1213-1230. doi:10.4208/nmtma.OA-2018-0122
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