  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.
