Motivated by dynamic risk measures and conditional $g$-expectations, in this work we propose a numerical method to approximate the solution operator given by a Backward Stochastic Differential Equation (BSDE). The main ingredients for this are the Wiener chaos decomposition and the classical Euler scheme for BSDEs. We show convergence of this scheme under very mild assumptions, and provide a rate of convergence in more restrictive cases. We then implement it using neural networks, and we present several numerical examples where we can check the accuracy of the method.

翻译：受动态风险测度和条件$g$-期望的启发，本文提出了一种数值方法来逼近由倒向随机微分方程（BSDE）给出的解算子。该方法的核心要素是维纳混沌分解和经典的BSDE欧拉格式。我们在非常温和的假设下证明了该格式的收敛性，并在更具限制性的情形下给出了收敛速率。随后，我们使用神经网络实现了该算法，并通过多个数值算例验证了方法的精度。