标题： 深度算子BSDE：一种近似解算子的数值方案 显示英文标题

标题： Deep Operator BSDE: a Numerical Scheme to Approximate the Solution Operators

摘要： 受动态风险度量和条件$g$-期望的启发，在本工作中我们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。 此方法的主要组成部分是维纳混沌分解和BSDE的经典欧拉方案。 我们在非常弱的假设下证明了该方案的收敛性，并在更严格的条件下提供了收敛速率。 然后我们使用神经网络实现它，并展示了几个数值例子，其中我们可以检查该方法的准确性。 显示英文摘要

摘要： 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.