Rough paths in idealized financial markets

Vladimir Vovk

Papers from arXiv.org

Abstract: This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume that the price path is positive and right-continuous. The qualification "typical" means that there is a trading strategy (constructed explicitly in the proof) that risks only one monetary unit but brings infinite capital when the variation index of the realized price path exceeds 2. The paper also reviews some known results for continuous price paths and lists several open problems.

Date: 2010-05, Revised 2016-11
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Published in Lithuanian Mathematical Journal 51(2):274-285, 2011

Downloads: (external link)
http://arxiv.org/pdf/1005.0279 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1005.0279

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().