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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 Łochowski. "On Truncated Variation of Brownian Motion with Drift." Bulletin of the Polish Academy of Sciences. Mathematics 56.3 (2008): 267-281. <http://eudml.org/doc/281146>.
@article{RafałŁochowski2008, abstract = {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.}, author = {Rafał Łochowski}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, keywords = {Brownian motion; variation}, language = {eng}, number = {3}, pages = {267-281}, title = {On Truncated Variation of Brownian Motion with Drift}, url = {http://eudml.org/doc/281146}, volume = {56}, year = {2008}, }
TY - JOUR AU - Rafał Łochowski TI - On Truncated Variation of Brownian Motion with Drift JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2008 VL - 56 IS - 3 SP - 267 EP - 281 AB - 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. LA - eng KW - Brownian motion; variation UR - http://eudml.org/doc/281146 ER -