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Multidimensional singular control and related Skorokhod problem: Sufficient conditions for the characterization of optimal controls

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  • Dianetti, Jodi
  • Ferrari, Giorgio

Abstract

We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The optimization problems concern the minimization of a discounted cost over an infinite time-horizon through a process of bounded variation affecting an Itô-diffusion. The setting is multidimensional, the drift of the state equation and the costs are convex, the volatility matrix can be constant or linear in the state. Our result applies to a relevant class of linear-quadratic models and it allows to construct the optimal control in degenerate and non degenerate settings considered in the literature.

Suggested Citation

  • Dianetti, Jodi & Ferrari, Giorgio, 2023. "Multidimensional singular control and related Skorokhod problem: Sufficient conditions for the characterization of optimal controls," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 547-592.
    • Handle: RePEc:eee:spapps:v:162:y:2023:i:c:p:547-592
    DOI: 10.1016/j.spa.2023.05.006
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    References listed on IDEAS

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    9. Tiziano De Angelis & Giorgio Ferrari & John Moriarty, 2019. "A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 512-531, May.
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    Cited by:

    1. Jodi Dianetti & Giorgio Ferrari & Renyuan Xu, 2024. "Exploratory Optimal Stopping: A Singular Control Formulation," Papers 2408.09335, arXiv.org, revised Oct 2024.

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