Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/7399
Title: Results on the supremum of fractional Brownian motion
Authors: Vardar, Ceren
Keywords: Fractional Brownian motion
Reflected fractional Brownian motion
Self similarity property
Hitting time
Gamma distribution
Hurst parameter
Markov's inequality
Jensen's inequality
Issue Date: 2011
Publisher: Hacettepe Univ, Fac Sci
Abstract: We show that the distribution of the square of the supremum of reflected fractional Brownian motion up to time a, with Hurst parameter-H greater than 1/2, is related to the distribution of its hitting time to level 1, using the self similarity property of fractional Brownian motion. It is also proven that the second moment of supremum of reflected fractional Brownian motion up to time a is bounded above by a(2H). Similar relations are obtained for the supremum of fractional Brownian motion with Hurst parameter greater than 1/2, and its hitting time to level 1. What is more, we obtain an upper bound on the complementary probability distribution of the supremum of fractional Brownian motion and reflected fractional Brownian motion up to time a, using Jensen's and Markov's inequalities. A sharper bound is observed on the distribution of the supremum of fractional Brownian motion by the properties of Gamma distribution. Finally, applications of the given results to financial markets are investigated, and partial results are provided.
URI: https://search.trdizin.gov.tr/yayin/detay/121521
https://hdl.handle.net/20.500.11851/7399
ISSN: 2651-477X
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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