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Stopping Times for Fractional Brownian Motion

In: Computational Management Science

Author

Listed:
  • Alexander V. Kulikov

    (Moscow Institute of Physics and Technology)

  • Pavel P. Gusyatnikov

    (Moscow Institute of Physics and Technology)

Abstract

In this article we consider an optimal stopping problem for the process of fractional Brownian motion. We prove that this problem for fractional Brownian motion has non trivial solution. We will describe a class of natural stopping times which compares increments of the process with a drift. We will show an example of non optimality of this class and consider a more complex class of stopping times which can be optimal.

Suggested Citation

  • Alexander V. Kulikov & Pavel P. Gusyatnikov, 2016. "Stopping Times for Fractional Brownian Motion," Lecture Notes in Economics and Mathematical Systems, in: Raquel J. Fonseca & Gerhard-Wilhelm Weber & João Telhada (ed.), Computational Management Science, edition 1, pages 195-200, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-20430-7_25
    DOI: 10.1007/978-3-319-20430-7_25
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    Cited by:

    1. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.

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