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arXiv · 2510.16599

A class of singular control problems with tipping points

Jean-Paul Décamps·Fabien Gensbittel·Thomas Mariotti·Stéphane Villeneuve
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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.

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Jean-Paul Décamps, Fabien Gensbittel, Thomas Mariotti, Stéphane Villeneuve. 2025-10-18. A class of singular control problems with tipping points. https://arxiv.org/abs/2510.16599

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