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A Class of Singular Control Problems with Tipping Points

Author

Listed:
  • Décamps, Jean-Paul
  • Gensbittel, Fabien
  • Mariotti, Thomas
  • Villeneuve, Stéphane

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.

Suggested Citation

  • Décamps, Jean-Paul & Gensbittel, Fabien & Mariotti, Thomas & Villeneuve, Stéphane, 2026. "A Class of Singular Control Problems with Tipping Points," CEPR Discussion Papers 21210, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:21210
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    File URL: https://cepr.org/publications/DP21210
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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