用深度神经算子统一建模概率系统，可直接预测期权最优行权边界。
Deep Neural Operator Learning for Probabilistic Models
- 构建神经算子架构，理论保证对广义概率模型的逼近能力
- 在欧式与美式期权定价中验证假设，覆盖带自由边界的偏微分方程
- 新敲定价下无需重新训练，即可生成最优停止边界
我们提出一种用于一般概率模型的深度神经算子框架。在算子在整个欧几里得空间上满足全局利普希茨条件，并针对一大类概率模型的情况下，建立了具有明确网络规模界限的通用逼近定理。所依赖的随机过程仅需满足可积性及一般尾概率条件。我们在前向-后向随机微分方程（FBSDE）框架下验证了欧式与美式期权定价问题中的这些假设，该框架涵盖了带有或不带自由边界的抛物型偏微分方程所产生的广泛算子。最后，我们通过一个美式期权组合的数值例子展示，学习到的模型可在不重新训练的前提下，为新的敲定价生成最优停止边界。
原文摘要 · Abstract (English)
We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal approximation theorem with explicit network-size bounds for the proposed architecture. The underlying stochastic processes are required only to satisfy integrability and general tail-probability conditions. We verify these assumptions for both European and American option-pricing problems within the forward-backward SDE (FBSDE) framework, which in turn covers a broad class of operators arising from parabolic PDEs, with or without free boundaries. Finally, we present a numerical example for a basket of American options, demonstrating that the learned model produces optimal stopping boundaries for new strike prices without retraining.
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