# Time Deep Gradient Flow Method for pricing American options

arXiv: https://arxiv.org/abs/2507.17606 · HTML: https://mlsanity.com/paper/2507.17606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 4 of 4)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [Solving high-dimensional optimal stopping problems using deep learning](https://mlsanity.com/paper/1908.01602/) (2019)
- [A time-stepping deep gradient flow method for option pricing in (rough) diffusion models](https://mlsanity.com/paper/2403.00746/) (2024)

## Abstract (arXiv)

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.