On the applicability of the maximality principle in optimal stopping: an example involving a diffusion and its running maximum

Neofytos Rodosthenous; Mihail Zervos

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arXiv · 2505.18394

On the applicability of the maximality principle in optimal stopping: an example involving a diffusion and its running maximum

Neofytos Rodosthenous·Mihail Zervos

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Abstract

The maximality principle has proved to be a valuable tool for identifying the optimal stopping boundaries in optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running maximum processes. The principle characterises the optimal stopping boundary as the maximal solution to a first-order nonlinear ODE that remains strictly below the diagonal in $\mathbb{R}^2$ or a "zero-level curve". In this paper, we construct a suitably tailored optimal stopping problem to which the maximality principle is not applicable.

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Neofytos Rodosthenous, Mihail Zervos. 2025-05-23. On the applicability of the maximality principle in optimal stopping: an example involving a diffusion and its running maximum. https://arxiv.org/abs/2505.18394

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