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Abstrakty
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
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Rocznik
Tom
Strony
267--281
Opis fizyczny
Bibliogr. 7 poz.
Twórcy
autor
- Department of Mathematical Economics, Warsaw School of Economics, Al. Niepodległości 162, 02-554 Warszawa, Poland, rlocho314@gmail.com
Bibliografia
- [1] A. N. Borodin and P. Salminen, Handbook of Brownian Motion. Facts and Formulae, Probab. Appl., Birkhäuser, Basel, 1996.
- [2] K. S. Chong, R. Cowan and L. Horst, The ruin problem and cover times of asymmetric random walks and Brownian motions, Adv. Appl. Probab. 32 (2000), 177-192.
- [3] W. Feller, The asymptotic distribution of the range of sums of independent random variables, Ann. Math. Statist. 22 (1952), 427-432.
- [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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0035-0009