Geodesic
On Truncated Variation of Brownian Motion with Drift
Rafał Łochowski1
1 Department of Mathematical Economics Warsaw School of Economics Al. Niepodległości 162 02-554 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 3, pp. 267-281

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba56-3-9
Keywords: introduce concept truncated variation brownian motion drift which differs regular variation neglecting small jumps smaller estimate expected value truncated variation behaviour resembling phase transition varies revealed truncated variation appears formula upper bound return trading based single asset flat commission

Rafał Łochowski 1

1 Department of Mathematical Economics Warsaw School of Economics Al. Niepodległości 162 02-554 Warszawa, Poland 
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Rafał Łochowski. On Truncated Variation of Brownian Motion with Drift. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 3, pp. 267-281. doi: 10.4064/ba56-3-9

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