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Mathematics > Optimization and Control

arXiv:2210.04645 (math)
[Submitted on 10 Oct 2022 (v1), last revised 23 Apr 2023 (this version, v2)]

Title:Optimal Stopping with Trees: The Details

Authors:Sigurd Assing, Xin Zhi
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Abstract:The purpose of this paper is two-fold, first, to review a recent method introduced by S. Becker, P. Cheridito, and P. Jentzen, for solving high-dimensional optimal stopping problems using deep Neural Networks, second, to propose an alternative algorithm replacing Neural Networks by CART-trees which allow for more interpretation of the estimated stopping rules. We in particular compare the performance of the two algorithms with respect to the Bermudan max-call benchmark example concluding that the Bermudan max-call may not be suitable to serve as a benchmark example for high-dimensional optimal stopping problems. We also show how our algorithm can be used to plot stopping boundaries.
Comments: 40 pages (including 18 figures and 10 tables)
Subjects: Optimization and Control (math.OC)
MSC classes: 60G40 (Primary) 65C20, 93E20 (Secondary)
Cite as: arXiv:2210.04645 [math.OC]
  (or arXiv:2210.04645v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.04645

Submission history

From: Sigurd Assing [view email]
[v1] Mon, 10 Oct 2022 12:46:19 UTC (578 KB)
[v2] Sun, 23 Apr 2023 11:17:17 UTC (578 KB)
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