In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations. The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving backward stochastic differential equations will be introduced and an upper error bound is established for the local regression. A full error analysis is also conducted for the explicit version of our algorithm and numerical experiments are performed to demonstrate various properties of our algorithm.

翻译：在这项工作中,我们应用了Stochastic 网格捆绑法(SGBM) 来从数字上解析后向随机差分方程式。 SGBM 算法基于有条件的预期近似值, 方法是将蒙特卡洛的样本路径捆绑在一起, 在每个捆包中进行局部递后后后回归回归回归回归。 将引入用于解决后向随机差分方程式的基本算法, 并为本地回归设定一个上限误差约束 。 还对我们的算法的清晰版本进行全面错误分析, 并进行数字实验, 以显示我们算法的各种特性 。