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Distribution of maximum loss of fractional Brownian motion with drift

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  • Caglar, Mine
  • Vardar-Acar, Ceren

Abstract

In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion with H≥1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0,t] behaves like the tail of the marginal distribution at time t.

Suggested Citation

  • Caglar, Mine & Vardar-Acar, Ceren, 2013. "Distribution of maximum loss of fractional Brownian motion with drift," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2729-2734.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2729-2734
    DOI: 10.1016/j.spl.2013.09.008
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    References listed on IDEAS

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    1. Hüsler, J. & Piterbarg, V., 1999. "Extremes of a certain class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 257-271, October.
    2. Libor Pospisil & Jan Vecer, 2010. "Portfolio sensitivity to changes in the maximum and the maximum drawdown," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 617-627.
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    Cited by:

    1. Vardar-Acar, Ceren & Bulut, Hatice, 2015. "Bounds on the expected value of maximum loss of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 117-122.

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