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Singular Control of the Drift of a Brownian System

Author

Listed:
  • Federico, Salvatore

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Schuhmann, Patrick

    (Center for Mathematical Economics, Bielefeld University)

Abstract
We consider a standard Brownian motion whose drift can be increased or decreased in a possibly singular manner. The objective is to minimize an expected functional involving the time-integral of a running cost and the proportional costs of adjusting the drift. The resulting two-dimensional degenerate singular stochastic control problem is solved by combining techniques of viscosity theory and free boundary problems. We provide a detailed description of the problem's value function and of the geometry of the state space, which is split into three regions by two monotone curves. Our main result shows that those curves are continuously di fferentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary diff erential equations.

Suggested Citation

  • Federico, Salvatore & Ferrari, Giorgio & Schuhmann, Patrick, 2020. "Singular Control of the Drift of a Brownian System," Center for Mathematical Economics Working Papers 637, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:637
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2943686/2943687
    File Function: First Version, 2020
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    References listed on IDEAS

    as
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    3. 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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    6. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    Full references (including those not matched with items on IDEAS)

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