Robust Multiple Stopping -- A Pathwise Duality Approach

TL;DR

This paper introduces a robust, pathwise duality-based method for solving complex optimal multiple stopping problems involving model uncertainty and jump-diffusions, providing convergent bounds and practical examples.

Contribution

It develops a novel theoretical framework with pathwise dual representations for robust multiple stopping, enabling numerical bounds that converge to the true solution.

Findings

Convergent upper and lower bounds for multiple stopping problems

Effective handling of model uncertainty in jump-diffusions

Practical examples demonstrating applicability

Abstract

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model uncertainty, and for general reward processes driven by multi-dimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem that satisfy appealing pathwise optimality (i.e., almost sure) 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 pre-limiting 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.