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A singular stochastic control problem with direction switching cost

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  • Łukasz Kruk

    (Maria Curie-Skłodowska University)

Abstract

We introduce a new class of singular stochastic control problems in which the process controller not only chooses the push intensity, at a price proportional to the displacement caused by his action, but he can also change the allowable control direction, paying a fixed cost for each such switching. Singular control of the one-dimensional Brownian motion with quadratic instantaneous cost function and costly direction switching on the infinite time horizon is analyzed in detail, leading to a closed-form solution. This example is used as an illustration of qualitative differences between the class of problems considered here and classic singular stochastic control.

Suggested Citation

  • Łukasz Kruk, 2023. "A singular stochastic control problem with direction switching cost," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(3), pages 325-349, December.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:3:d:10.1007_s00186-023-00839-8
    DOI: 10.1007/s00186-023-00839-8
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    References listed on IDEAS

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    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. Boetius, Frederik & Kohlmann, Michael, 1998. "Connections between optimal stopping and singular stochastic control," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 253-281, September.
    3. Gaïgi, M’hamed & Ly Vath, Vathana & Scotti, Simone, 2022. "Optimal harvesting under marine reserves and uncertain environment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1181-1194.
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