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Volume 22, Issue 6
A Class of Runge-Kutta Methods for Backward Stochastic Differential Equations

Xiao Tang & Jie Xiong

DOI: 10.4208/ijnam2025-1034

Int. J. Numer. Anal. Mod., 22 (2025), pp. 777-800.

Published online: 2025-08

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  • Abstract

In this paper, we introduce a class of Runge-Kutta (RK) methods for backward stochastic differential equations (BSDEs). The convergence rate is studied and the corresponding order conditions are obtained. For the conditional expectations involved in the methods, we design an approximation algorithm by combining the characteristics of the methods and replacing the increments of Brownian motion with appropriate discrete random variables. An important feature of our approximation algorithm is that interpolation operations can be avoided. The numerical results of four examples are presented to show that our RK methods provide a good approach for solving the BSDEs.

  • Keywords

Backward stochastic differential equations, Runge-Kutta methods, order condition, conditional expectation.

  • AMS Subject Headings

60H10, 65L06, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-22-777, author = {Tang , Xiao and Xiong , Jie}, title = {A Class of Runge-Kutta Methods for Backward Stochastic Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2025}, volume = {22}, number = {6}, pages = {777--800}, abstract = {

In this paper, we introduce a class of Runge-Kutta (RK) methods for backward stochastic differential equations (BSDEs). The convergence rate is studied and the corresponding order conditions are obtained. For the conditional expectations involved in the methods, we design an approximation algorithm by combining the characteristics of the methods and replacing the increments of Brownian motion with appropriate discrete random variables. An important feature of our approximation algorithm is that interpolation operations can be avoided. The numerical results of four examples are presented to show that our RK methods provide a good approach for solving the BSDEs.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1034}, url = {http://global-sci.org/intro/article_detail/ijnam/24293.html} }
TY - JOUR T1 - A Class of Runge-Kutta Methods for Backward Stochastic Differential Equations AU - Tang , Xiao AU - Xiong , Jie JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 777 EP - 800 PY - 2025 DA - 2025/08 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1034 UR - https://global-sci.org/intro/article_detail/ijnam/24293.html KW - Backward stochastic differential equations, Runge-Kutta methods, order condition, conditional expectation. AB -

In this paper, we introduce a class of Runge-Kutta (RK) methods for backward stochastic differential equations (BSDEs). The convergence rate is studied and the corresponding order conditions are obtained. For the conditional expectations involved in the methods, we design an approximation algorithm by combining the characteristics of the methods and replacing the increments of Brownian motion with appropriate discrete random variables. An important feature of our approximation algorithm is that interpolation operations can be avoided. The numerical results of four examples are presented to show that our RK methods provide a good approach for solving the BSDEs.

Tang , Xiao and Xiong , Jie. (2025). A Class of Runge-Kutta Methods for Backward Stochastic Differential Equations. International Journal of Numerical Analysis and Modeling. 22 (6). 777-800. doi:10.4208/ijnam2025-1034
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