用深度学习求解非马尔可夫下的全耦合随机微分方程，可处理复杂金融问题。
A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications
- 提出基于深度学习的非马尔可夫全耦合正向-反向随机微分方程求解方法
- 给出误差估计与收敛性分析，数值验证了在粗糙波动率下的效用最大化求解能力
- 适合研究复杂金融模型与随机控制的科研人员参考
本文将基于深度学习的数值方法扩展至非马尔可夫框架下的全耦合前向-反向随机微分方程（FBSDEs）。与现有工作不同，该方法不仅分析非马尔可夫情形，还处理全耦合设置：前向过程的漂移与扩散系数均可为随机，并依赖于反向分量 $Y$ 和 $Z$。同时，通过在粗糙波动率下的效用最大化问题中应用所提方法，展示了其实际可行性。数值实验验证了算法的有效性。
原文摘要 · Abstract (English)
In this work, we extend deep learning-based numerical methods to fully coupled forward-backward stochastic differential equations (FBSDEs) within a non-Markovian framework. Error estimates and convergence are provided. In contrast to the existing literature, our approach not only analyzes the non-Markovian framework but also addresses fully coupled settings, in which both the drift and diffusion coefficients of the forward process may be random and depend on the backward components $Y$ and $Z$. Furthermore, we illustrate the practical applicability of our framework by addressing utility maximization problems under rough volatility, which are solved numerically with the proposed deep learning-based methods.
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