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Volume 17, Issue 6
An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations

Xiao Tang & Jie Xiong

Adv. Appl. Math. Mech., 17 (2025), pp. 1682-1714.

Published online: 2025-09

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  • Abstract

This paper proposes an explicit method for the coupled forward backward stochastic differential equations (FBSDEs). Our method combines skillfully a weak second order stochastic Runge-Kutta method for solving forward equations with a two-step method for solving backward equations. We give a convergence theorem for the proposed method when the FBSDEs is weakly coupled (the forward equations are independent of the variable Z). Finally, some numerical results are presented, and the numerical results show that our method still works well even if the forward equations depend on Z.

  • AMS Subject Headings

65C30, 60H10, 65L06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-17-1682, author = {Tang , Xiao and Xiong , Jie}, title = {An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {17}, number = {6}, pages = {1682--1714}, abstract = {

This paper proposes an explicit method for the coupled forward backward stochastic differential equations (FBSDEs). Our method combines skillfully a weak second order stochastic Runge-Kutta method for solving forward equations with a two-step method for solving backward equations. We give a convergence theorem for the proposed method when the FBSDEs is weakly coupled (the forward equations are independent of the variable Z). Finally, some numerical results are presented, and the numerical results show that our method still works well even if the forward equations depend on Z.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2024-0026}, url = {http://global-sci.org/intro/article_detail/aamm/24491.html} }
TY - JOUR T1 - An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations AU - Tang , Xiao AU - Xiong , Jie JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1682 EP - 1714 PY - 2025 DA - 2025/09 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2024-0026 UR - https://global-sci.org/intro/article_detail/aamm/24491.html KW - Forward backward stochastic differential equations, explicit method, convergence. AB -

This paper proposes an explicit method for the coupled forward backward stochastic differential equations (FBSDEs). Our method combines skillfully a weak second order stochastic Runge-Kutta method for solving forward equations with a two-step method for solving backward equations. We give a convergence theorem for the proposed method when the FBSDEs is weakly coupled (the forward equations are independent of the variable Z). Finally, some numerical results are presented, and the numerical results show that our method still works well even if the forward equations depend on Z.

Tang , Xiao and Xiong , Jie. (2025). An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations. Advances in Applied Mathematics and Mechanics. 17 (6). 1682-1714. doi:10.4208/aamm.OA-2024-0026
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