用神经网络逼近随机微分方程解算子，高效求解动态风险评估问题。
Deep Operator BSDE: a Numerical Scheme to Approximate Solution Operators
- 结合威纳混沌分解与欧拉格式，构造新型数值方法
- 在弱假设下保证收敛性，强假设下给出收敛速率
- 适用于金融风险建模等需解算子的场景
受动态风险度量和条件g-期望启发，本文提出一种数值方法，用于逼近由倒向随机微分方程（BSDE）定义的解算子。核心思想是结合威纳混沌分解与经典的欧拉数值方案。在非常温和的假设下证明了该方法的收敛性，并在更严格的条件下给出了收敛速率。随后，采用神经网络实现该算法，并通过多个数值实验验证了方法的准确性。
原文摘要 · Abstract (English)
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.
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