30th of September - Niklas Dexheimer (VU Amsterdam)
Title: Data-Driven Optimal Stopping of Diffusion Processes
Abstract: The standard theory of optimal stopping is based on the idealised assumption that the underlying process is essentially known. We drop this restriction and study data-driven optimal stopping for a general diffusion process, focusing on investigating the statistical performance of the proposed estimator of the optimal stopping barrier. We first derive non-asymptotic upper bounds on the simple regret, along with uniform and non-asymptotic PAC bounds. Minimax optimality is verified by completing the upper bound results with matching lower bounds on the simple regret. We also investigate how our results on the simple regret transfer to the cumulative regret for a specific exploration-exploitation strategy. In order to improve the bound for the cumulative regret we also present an online strategy aimed at estimating the optimal stopping barrier.