# Optimal Stopping via Randomized Neural Networks

arXiv: https://arxiv.org/abs/2104.13669 · HTML: https://mlsanity.com/paper/2104.13669/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 80 references that are in the map.
- First posted on arXiv 28 Apr 2021.

## Builds on (most cited first, 3 of 3)

- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [Pricing high-dimensional Bermudan options with hierarchical tensor formats](https://mlsanity.com/paper/2103.01934/) (2021)
- [On Lenglart's Theory of Meyer-sigma-fields and El Karoui's Theory of Optimal Stopping](https://mlsanity.com/paper/1810.08485/) (2018)

## Built on by (most cited first, 28 of 28)

- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Universal approximation property of Banach space-valued random feature models including random neural networks](https://mlsanity.com/paper/2312.08410/) (2023)
- [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)
- [Learning to Optimally Stop Diffusion Processes, with Financial Applications](https://mlsanity.com/paper/2408.09242/) (2024)
- [A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression](https://mlsanity.com/paper/2310.00987/) (2023)
- [Deep Signature Algorithm for Multi-dimensional Path-Dependent Options](https://mlsanity.com/paper/2211.11691/) (2022)
- [Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion](https://mlsanity.com/paper/2411.03384/) (2024)
- [Universal Regular Conditional Distributions](https://mlsanity.com/paper/2105.07743/) (2021)
- [Random Feature Representation Boosting](https://mlsanity.com/paper/2501.18283/) (2025)
- [Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks](https://mlsanity.com/paper/2302.12439/) (2023)
- [How (Implicit) Regularization of ReLU Neural Networks Characterizes the Learned Function -- Part II: the Multi-D Case of Two Layers with Random First Layer](https://mlsanity.com/paper/2303.11454/) (2023)
- [RandNet-Parareal: a time-parallel PDE solver using Random Neural Networks](https://mlsanity.com/paper/2411.06225/) (2024)
- [Deep Neural Operator Learning for Probabilistic Models](https://mlsanity.com/paper/2511.07235/) (2025)
- [Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks](https://mlsanity.com/paper/2301.08232/) (2023)
- [Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing](https://mlsanity.com/paper/2309.04557/) (2023)
- [Quantum-Inspired Tensor Neural Networks for Option Pricing](https://mlsanity.com/paper/2212.14076/) (2022)
- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [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)
- [Learning to Liquidate Forex: Optimal Stopping via Adaptive Top-K Regression](https://mlsanity.com/paper/2202.12578/) (2022)
- [Scalable Signature-Based Distribution Regression via Reference Sets](https://mlsanity.com/paper/2410.09196/) (2024)
- [Time Deep Gradient Flow Method for pricing American options](https://mlsanity.com/paper/2507.17606/) (2025)
- [Reinforcement Learning in Real Option Models](https://mlsanity.com/paper/2602.15643/) (2026)
- [Continuous-time Optimal Stopping through Deep Reinforcement Learning](https://mlsanity.com/paper/2606.17545/) (2026)
- [CC-AOS: Cost- and Horizon-Conditioned Amortized Backward Induction for Finite-Horizon Optimal Stopping](https://mlsanity.com/paper/2607.22774/) (2026)
- [Deep Learning for Reflected BSDEs: Regularization and Error Analysis](https://mlsanity.com/paper/2609.05434/) (2026)

## Abstract (arXiv)

This paper presents the benefits of using randomized neural networks instead of standard basis functions or deep neural networks to approximate the solutions of optimal stopping problems. The key idea is to use neural networks, where the parameters of the hidden layers are generated randomly and only the last layer is trained, in order to approximate the continuation value. Our approaches are applicable to high dimensional problems where the existing approaches become increasingly impractical. In addition, since our approaches can be optimized using simple linear regression, they are easy to implement and theoretical guarantees can be provided. We test our approaches for American option pricing on Black--Scholes, Heston and rough Heston models and for optimally stopping a fractional Brownian motion. In all cases, our algorithms outperform the state-of-the-art and other relevant machine learning approaches in terms of computation time while achieving comparable results. Moreover, we show that they can also be used to efficiently compute Greeks of American options.