Volatility and arbitrage

E. Robert Fernholz, Ioannis Karatzas and Johannes Ruf

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: The capitalization-weighted cumulative variation d i=1 0 µi(t)d(log µi)(t) in an equity market consisting of a fixed number d of assets with capitalization weights µi(·) ; is an observable and a nondecreasing function of time. If this observable of the market is not just nondecreasing but actually grows at a rate bounded away from zero, then strong arbitrage can be constructed relative to the market over sufficiently long time horizons. It has been an open issue for more than ten years, whether such strong outperformance of the market is possible also over arbitrary time horizons under the stated condition. We show that this is not possible in general, thus settling this long-open question. We also show that, under appropriate additional conditions, outperformance over any time horizon indeed becomes possible, and exhibit investment strategies that effect it.

Keywords: trading strategies; functional generation; relative arbitrage; short-term arbitrage; support of diffusions; diffusions on manifolds; nondegeneracy (search for similar items in EconPapers)
JEL-codes: C1 J1 (search for similar items in EconPapers)
Date: 2018-02-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Published in Annals of Applied Probability, 1, February, 2018, 28(1), pp. 378-417. ISSN: 1050-5164

Downloads: (external link)
http://eprints.lse.ac.uk/75234/ Open access 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:ehl:lserod:75234

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().