Optimal Stopping via Randomized Neural Networks
This provides a more efficient method for practitioners in finance dealing with high-dimensional optimal stopping, such as American option pricing, though it is incremental in applying randomized neural networks to this domain.
The paper tackled the problem of solving high-dimensional optimal stopping problems by using randomized neural networks to approximate continuation values, achieving comparable results to state-of-the-art methods with significantly faster computation times in tests on models like Black-Scholes and Heston.
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.