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On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift
Date
2013-08-15
Author
Vardar Acar, Ceren
Zirbel, Craig L.
Szekely, Gabor J.
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Applied Mathematics
,
Computational Mathematics
URI
https://hdl.handle.net/11511/48664
Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
https://doi.org/10.1016/j.cam.2013.01.010
Collections
Department of Statistics, Article
Citation Formats
IEEE
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BibTeX
C. Vardar Acar, C. L. Zirbel, and G. J. Szekely, “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
, vol. 248, pp. 61–75, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48664.