A class of singular control problems with tipping points
Optimization and Control
2026-02-25 v2
Abstract
Tipping points characterize situations where a regulated system may experience a sudden and irreversible change and are generally associated with a random state of the system below which the change materializes. In this paper, we study a singular stochastic control problem in which the performance criterion depends on the hitting time of a random state that is not a stopping time for the reference filtration. We establish a connection between the value of this problem and that of a singular control problem involving a diffusion and its running minimum. We provide a verification lemma that we apply to explicitly solve a resource-extraction problem with an ex-ante unknown tipping point.
Cite
@article{arxiv.2510.16599,
title = {A class of singular control problems with tipping points},
author = {Jean-Paul Décamps and Fabien Gensbittel and Thomas Mariotti and Stéphane Villeneuve},
journal= {arXiv preprint arXiv:2510.16599},
year = {2026}
}