Optimal Stopping via Randomized Neural Networks

TL;DR

This paper introduces a randomized neural network approach for optimal stopping problems, offering a practical, efficient, and theoretically sound method that outperforms existing techniques in high-dimensional settings.

Contribution

The paper proposes a novel randomized neural network method for optimal stopping, simplifying implementation and providing theoretical guarantees, especially effective in high-dimensional problems.

Findings

Outperforms state-of-the-art in American option pricing

Efficiently computes Greeks of American options

Applicable to high-dimensional problems with theoretical guarantees

Abstract

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.