# Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks

arXiv: https://arxiv.org/abs/2302.12439 · HTML: https://mlsanity.com/paper/2302.12439/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 62 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 13 of 13)

- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [An overview on deep learning-based approximation methods for partial differential equations](https://mlsanity.com/paper/2012.12348/) (2020)
- [Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations](https://mlsanity.com/paper/1804.07010/) (2018)
- [Machine Learning for semi linear PDEs](https://mlsanity.com/paper/1809.07609/) (2018)
- [Optimal Stopping via Randomized Neural Networks](https://mlsanity.com/paper/2104.13669/) (2021)
- [Neural networks-based algorithms for stochastic control and PDEs in finance](https://mlsanity.com/paper/2101.08068/) (2021)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions](https://mlsanity.com/paper/1909.11532/) (2019)
- [Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems](https://mlsanity.com/paper/2210.04118/) (2022)
- [Deep neural network expressivity for optimal stopping problems](https://mlsanity.com/paper/2210.10443/) (2022)
- [Randomized optimal stopping algorithms and their convergence analysis](https://mlsanity.com/paper/2002.00816/) (2020)
- [Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks](https://mlsanity.com/paper/2301.08232/) (2023)
- [Kriging Metamodels and Experimental Design for Bermudan Option Pricing](https://mlsanity.com/paper/1509.02179/) (2015)

## Built on by (most cited first, 3 of 3)

- [DeepMartingale: Duality of the Optimal Stopping Problem with Expressivity and High-Dimensional Hedging](https://mlsanity.com/paper/2510.13868/) (2025)
- [Deep Learning for the Multiple Optimal Stopping Problem](https://mlsanity.com/paper/2512.22961/) (2025)
- [Continuous-time Optimal Stopping through Deep Reinforcement Learning](https://mlsanity.com/paper/2606.17545/) (2026)

## Abstract (arXiv)

In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural networks to simultaneously compute both the lower and upper bounds of the option price, and the second one accomplishes the same goal with one global network. The avoidance of extra simulations and the use of neural networks significantly reduce the computational complexity and allow us to price Bermudan options with frequent exercise opportunities in high dimensions, as illustrated by the provided numerical experiments. As a by-product, these methods also derive a hedging strategy for the option, which can also be used as a control variate for variance reduction.