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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 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.

Suggested Citation

  • Décamps, Jean-Paul & Gensbittel, Fabien & Mariotti, Thomas & Villeneuve, Stéphane, 2025. "A Class of Singular Control Problems with Tipping Points," TSE Working Papers 25-1694, Toulouse School of Economics (TSE), revised Feb 2026.
    • Handle: RePEc:tse:wpaper:131174
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    References listed on IDEAS

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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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