Décamps, Jean-Paul, Gensbittel, FabienORCID: https://orcid.org/0000-0002-0949-9456, Mariotti, ThomasORCID: https://orcid.org/0000-0002-0525-8743 and Villeneuve, StéphaneORCID: https://orcid.org/0000-0003-3213-1905 (2025) A class of singular control problems with tipping points. TSE Working Paper, n. 25-1694, Toulouse

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Abstract

Tipping points define situations where a system experiences sudden and irreversible changes and are generally associated with a random level of the system below which the changes materialize. In this paper, we study a singular stochastic control problem in which the performance criterion depends on the hitting time of a random level that is not a stopping time for the reference filtration. We establish a connection between the value of the problem and the value of a singular control problem involving a diffusion and its running minimum. We prove a verification theorem and apply our results to explicitly solve a resource extraction problem where the random evolution of the resource changes when it crosses a tipping point.