Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/1718
Title: On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift
Authors: Acar, Ceren Vardar
Zirbel, Craig L.
Székely, Gábor J.
142337
Keywords: Brownian motion with drift
 Scaling property
 Uniform continuity
 Markov property
 Correlation coefficient
Issue Date: Aug-2013
Publisher: Elsevier Science Bv
Source: Vardar-Acar, C., Zirbel, C. L., & Székely, G. J. (2013). On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift. Journal of Computational and Applied Mathematics, 248, 61-75.
Abstract: Investors are naturally interested in the supremum and the infimum of stock prices, also in the maximum gain and the maximum loss over a time period. To shed light on these relatively complicated aspects of sample paths, we consider Brownian motion with and without drift. We provide explicit calculations of the correlation between the supremum and the infimum of Brownian motion with drift. We establish a number of results concerning the distributions of maximum gain and maximum loss. We present simulation studies of maximum gain and of maximum loss of Brownian motion with a range of values for the drift. We conjecture that the correlation between maximum gain and maximum loss has a minimum value of -0.5 at drift 2.
URI: https://doi.org/10.1016/j.cam.2013.01.010
https://hdl.handle.net/20.500.11851/1718
ISSN: 0377-0427
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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