Robust Multiple Stopping—A Duality Approach

Roger Laeven, John G. M. Schoenmakers (), Nikolaus Schweizer () and Mitja Stadje ()
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John G. M. Schoenmakers: Stochastic Algorithms and Nonparametric Statistics, Weierstrass Institute Berlin, D-10117 Berlin, Germany
Nikolaus Schweizer: Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, Netherlands
Mitja Stadje: Institute of Insurance Science and Institute of Mathematical Finance, Faculty of Mathematics and Economics, Ulm University, D-89069 Ulm, Germany

Mathematics of Operations Research, 2025, vol. 50, issue 2, 1250-1276

Abstract: We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights—that is, optimal multiple stopping—for a robust evaluation that accounts for model uncertainty with a dominated family of priors and for general reward processes driven by multidimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem that satisfy appealing almost sure pathwise optimality properties. Next, we exploit these theoretical results to develop upper and lower bounds that, as we formally show, not only converge to the true solution asymptotically, but also constitute genuine prelimiting upper and lower bounds. We illustrate the applicability of our approach in a few examples and analyze the impact of model uncertainty on optimal multiple stopping strategies.

Keywords: Primary: 49L20; 60G40; 62L15; optimal stopping; multiple stopping; robustness; model uncertainty; ambiguity; pathwise duality; g -expectations; BSDEs; regression (search for similar items in EconPapers)
Date: 2025
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http://dx.doi.org/10.1287/moor.2021.0237 (application/pdf)

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Working Paper: Robust multiple stopping — A duality approach (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:2:p:1250-1276

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