On truncated variation of Brownian motion with drift

• Autorzy: Łochowski R.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Brownian motion; variation

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 3-4
• Strony: 267--281
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Łochowski R.

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

Bibliografia

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• [4] P. Levy, Le mouvement brownien plane, Amer. J. Math. 62 (1940), 487-550.
• [5] H. O. Pollak, A remark on “Elementary inequalities for Mills’ ratio” by Yûsaku Komatu, Rep. Statist. Appl. Res. Un. Jap. Sci. Engrs. 4 (1955-57), 110.
• [6] E. Tanre and P. Vallois, Range of Brownian motion with drift, J. Theoret. Probab. 19 (2006), 45-69.
• [7] H. M. Taylor, A stopped Brownian motion formula, Ann. Probab. 3 (1975), 234-246.