Robust Multiple Stopping—A Duality Approach

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. Funding: R. J. A. Laeven received financial support from the Netherlands Organization for Scientific Research (NWO) [Grants NWO-Vidi and NWO-Vici]. J. G. M. Schoenmakers received financial support from the Deutsche Forschungsgemeinschaft Excellence Cluster Math+ Berlin [Project AA4-2]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0237 .