  We propose a novel group of Gaussian Process based algorithms for fast
approximate optimal stopping of time series with specific applications to
financial markets. We show that structural properties commonly exhibited by
financial time series (e.g., the tendency to mean-revert) allow the use of
Gaussian and Deep Gaussian Process models that further enable us to
analytically evaluate optimal stopping value functions and policies. We
additionally quantify uncertainty in the value function by propagating the
price model through the optimal stopping analysis. We compare and contrast our
proposed methods against a sampling-based method, as well as a deep learning
based benchmark that is currently considered the state-of-the-art in the
literature. We show that our family of algorithms outperforms benchmarks on
three historical time series datasets that include intra-day and end-of-day
equity stock prices as well as the daily US treasury yield curve rates.
