论文标题
PDGM：一种神经网络方法，用于求解路径依赖的偏微分方程
PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations
论文作者
论文摘要
在本文中，我们提出了一种用于路径依赖性偏微分方程（PPDE）的新型数值方法。这些方程式首先出现在Dupire [2009]的开创性工作中，其中开发了功能性的ITOculus来处理依赖路径依赖的金融衍生品合同。更具体的说法，我们将Sirignano和Spiliopoulos [2018]的深层艺术方法（DGM）推广到处理这些方程式。我们称之为路径依赖性DGM（PDGM）的方法包括使用馈送前向前和长短期内存体系结构的组合来建模PPDE的解决方案。然后，我们分析了几个数值示例，其中许多来自金融数学文献，这些数字在非常不同的情况下表明了该方法的能力。
In this paper, we propose a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [2009], where the functional Itô calculus was developed to deal with path-dependent financial derivatives contracts. More specificaly, we generalize the Deep Galerking Method (DGM) of Sirignano and Spiliopoulos [2018] to deal with these equations. The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE. We then analyze several numerical examples, many from the Financial Mathematics literature, that show the capabilities of the method under very different situations.
