Advertisement

Stopping Times for Fractional Brownian Motion

  • Alexander V. Kulikov
  • Pavel P. Gusyatnikov
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 682)

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.

References

  1. 1.
    Cheridito, P.: Arbitrage in fractional brownian motion models. Finance Stochast. 7(4), 533–553 (2003)CrossRefGoogle Scholar
  2. 2.
    Dieker, T.: Simulation of fractional brownian motion. Master’s thesis, Department of Mathematical Sciences, University of Twente, Enschede (2004)Google Scholar
  3. 3.
    Guasoni, P.: No arbitrage under transaction costs, with fractional brownian motion and beyond. Math. Financ. 16(3), 569–582 (2006)CrossRefGoogle Scholar
  4. 4.
    Mandelbrot, B., van Ness, J.W.: Fractional brownian motions, fractional noises and applications. SIAM Rev. 10(4), 422–437 (1968)CrossRefGoogle Scholar
  5. 5.
    Shiryaev, A., Xu, Z., Zhou, X.Y.: Thou shalt buy and hold. Quant. Finance 8(8), 765–776 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyMoscowRussia

Personalised recommendations