On Truncated Variation of Brownian Motion with Drift

Volume 56 / 2008

Rafał Łochowski Bulletin Polish Acad. Sci. Math. 56 (2008), 267-281 MSC: Primary 60G15. DOI: 10.4064/ba56-3-9


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.


  • Rafał ŁochowskiDepartment of Mathematical Economics
    Warsaw School of Economics
    Al. Niepodległości 162
    02-554 Warszawa, Poland

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