A class of singular control problems with tipping points.”

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.

Reference

Jean-Paul Décamps, Fabien Gensbittel, Thomas Mariotti, and Stéphane Villeneuve, “A class of singular control problems with tipping points.””, TSE Working Paper, n. 25-1694, October 2025.