In this work we propose a new algorithm for solving high-dimensional backward stochastic differential equations (BSDEs). Based on the general theta-discretization for the time-integrands, we show how to efficiently use eXtreme Gradient Boosting (XGBoost) regression to approximate the resulting conditional expectations in a quite high dimension. Numerical results illustrate the efficiency and accuracy of our proposed algorithms for solving very high-dimensional (up to $10000$ dimensions) nonlinear BSDEs.

翻译：在这项工作中,我们提出了一个新的算法,用于解决高维的后向随机差分方程式(BSDEs ) 。 根据时间-内格朗的全方位分解法,我们展示了如何有效地使用 eXtreme Gradient 推进(XGBoost) 回归法, 以相当高的维度来接近由此产生的有条件期望。 数字结果显示了我们为解决非常高维(高达1,000美元维度)的非线性 BSDEs而提议的算法的效率和准确性。