This paper presents new machine learning approaches to approximate the solutions of optimal stopping problems. The key idea of these methods 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 are provided. Our randomized reinforcement learning approach and randomized recurrent neural network approach outperform the state-of-the-art and other relevant machine learning approaches in Markovian and non-Markovian examples, respectively. In particular, we test our approaches on Black-Scholes, Heston, rough Heston and fractional Brownian motion. Moreover, we show that they can also be used to efficiently compute Greeks of American options.

翻译：本文提出了新的机器学习方法来逼近最优停时问题的解。这些方法的核心思想是利用神经网络——其中隐藏层参数随机生成，仅训练最后一层——来逼近延续价值。我们的方法适用于现有方法日益不实用化的高维问题。此外，由于可采用简单线性回归进行优化，这些方法易于实现，并提供了理论保证。我们的随机化强化学习方法和随机化循环神经网络方法分别在马尔可夫与非马尔可夫示例中超越了现有最优技术及其他相关机器学习方法。特别地，我们在Black-Scholes、Heston、粗糙Heston及分数布朗运动模型上进行了测试。此外，我们还证明了这些方法可有效用于计算美式期权的希腊值。