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 - <p style="text-align: justify;">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.</p>