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Robust Multiple Stopping—A Duality Approach

Author

Listed:
  • Roger J. A. Laeven

    (Department of Quantitative Economics, University of Amsterdam, 1001 NJ Amsterdam, Netherlands)

  • 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)

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.

Suggested Citation

  • Roger J. A. Laeven & John G. M. Schoenmakers & Nikolaus Schweizer & Mitja Stadje, 2025. "Robust Multiple Stopping—A Duality Approach," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1250-1276, May.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:2:p:1250-1276
    DOI: 10.1287/moor.2021.0237
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