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Volume 13, Issue 6
Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations

Quan Zhou & Yabing Sun

DOI: 10.4208/aamm.OA-2020-0133

Adv. Appl. Math. Mech., 13 (2021), pp. 1293-1317.

Published online: 2021-08

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  • Abstract

By using the Feynman-Kac formula and combining with Itô-Taylor expansion and finite difference approximation, we first develop an explicit third order one-step method for solving decoupled forward backward stochastic differential equations. Then based on the third order one, an explicit fourth order method is further proposed. Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.

  • Keywords

Decoupled forward backward stochastic differential equations, Itô-Taylor expansion, finite difference approximation, explicit one-step method, high order convergence.

  • AMS Subject Headings

65C20, 65C30, 60H35, 65H30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-1293, author = {Zhou , Quan and Sun , Yabing}, title = {Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {6}, pages = {1293--1317}, abstract = {

By using the Feynman-Kac formula and combining with Itô-Taylor expansion and finite difference approximation, we first develop an explicit third order one-step method for solving decoupled forward backward stochastic differential equations. Then based on the third order one, an explicit fourth order method is further proposed. Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0133}, url = {http://global-sci.org/intro/article_detail/aamm/19424.html} }
TY - JOUR T1 - Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations AU - Zhou , Quan AU - Sun , Yabing JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1293 EP - 1317 PY - 2021 DA - 2021/08 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0133 UR - https://global-sci.org/intro/article_detail/aamm/19424.html KW - Decoupled forward backward stochastic differential equations, Itô-Taylor expansion, finite difference approximation, explicit one-step method, high order convergence. AB -

By using the Feynman-Kac formula and combining with Itô-Taylor expansion and finite difference approximation, we first develop an explicit third order one-step method for solving decoupled forward backward stochastic differential equations. Then based on the third order one, an explicit fourth order method is further proposed. Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.

Zhou , Quan and Sun , Yabing. (2021). Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations. Advances in Applied Mathematics and Mechanics. 13 (6). 1293-1317. doi:10.4208/aamm.OA-2020-0133
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