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Connections between optimal stopping and singular stochastic control

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  • Boetius, Frederik
  • Kohlmann, Michael
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    Abstract

    We consider an optimal control problem for an Itô diffusion and a related stopping problem. Their value functions satisfy (d/dx)V=u and an optimal control defines an optimal stopping time. Conversely, we construct an optimal control from optimal stopping times, find a representation of V as an integral of u and describe the optimal state as a reflected process.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(98)00049-0
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 77 (1998)
    Issue (Month): 2 (September)
    Pages: 253-281

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    Handle: RePEc:eee:spapps:v:77:y:1998:i:2:p:253-281
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    Keywords: Singular control Optimal stopping Impulse control Local times Irreversible investment Options;

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    1. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
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    Cited by:

    1. de Angelis, Tiziano & Federico, Salvatore & Ferrari, Giorgio, 2016. "On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment," Center for Mathematical Economics Working Papers 509, Center for Mathematical Economics, Bielefeld University.
    2. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
    3. Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
    4. Tiziano De Angelis & Erik Ekstr\"om, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Jul 2017.
    5. de Angelis, Tiziano & Ferrari, Giorgio, 2016. "Stochastic nonzero-sum games: a new connection between singular control and optimal stopping," Center for Mathematical Economics Working Papers 565, Center for Mathematical Economics, Bielefeld University.
    6. Tiziano De Angelis & Salvatore Federico & Giorgio Ferrari, 2014. "Optimal Boundary Surface for Irreversible Investment with Stochastic Costs," Papers 1406.4297, arXiv.org, revised Jan 2017.
    7. Xin Guo & Pascal Tomecek, 2008. "Solving Singular Control from Optimal Switching," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(1), pages 25-45, March.

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