We introduce the concept of truncated variation of Brownian motion with drift, which differs from regular variation by neglecting small jumps (smaller than some c > 0). We estimate the expected value of the truncated variation. The behaviour resembling phase transition as c varies is revealed. Truncated variation appears in the formula for an upper bound for return from any trading based on a single asset with flat commission.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-9,
author = {Rafa\l\ \L ochowski},
title = {On Truncated Variation of Brownian Motion with Drift},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {56},
year = {2008},
pages = {267-281},
zbl = {1158.60011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-9}
}
Rafał Łochowski. On Truncated Variation of Brownian Motion with Drift. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 267-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-9/