标题： 时间深度梯度流方法用于定价美式期权 显示英文标题

标题： Time Deep Gradient Flow Method for pricing American options

摘要： 在这项研究中，我们探索了基于神经网络的方法，在BlackScholes和Heston模型下对多维美式看跌期权进行定价，扩展到五个维度。 我们关注两种方法：时间深度梯度流（TDGF）方法和深度伽辽金方法（DGM）。 我们将TDGF方法扩展以处理美式期权中固有的自由边界偏微分方程。 我们在训练过程中精心设计了采样策略以提高性能。 TDGF和DGM都实现了高精度，并且在计算速度方面优于传统的蒙特卡洛方法。 特别是，TDGF在训练期间通常比DGM更快。 显示英文摘要

摘要： In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow (TDGF) method and the Deep Galerkin Method (DGM). We extend the TDGF method to handle the free-boundary partial differential equation inherent in American options. We carefully design the sampling strategy during training to enhance performance. Both TDGF and DGM achieve high accuracy while outperforming conventional Monte Carlo methods in terms of computational speed. In particular, TDGF tends to be faster during training than DGM.