{"ID":2853477,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.16599","arxiv_id":"2510.16599","title":"A class of singular control problems with tipping points","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.16599","url_pdf":"https://arxiv.org/pdf/2510.16599v2","authors":"[\"Jean-Paul Décamps\",\"Fabien Gensbittel\",\"Thomas Mariotti\",\"Stéphane Villeneuve\"]","published":"2025-10-18T17:55:37Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}