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Volatility and arbitrage

Fernholz, E. Robert, Karatzas, Ioannis and Ruf, Johannes ORCID: 0000-0003-3616-2194 (2018) Volatility and arbitrage. Annals of Applied Probability, 28 (1). pp. 378-417. ISSN 1050-5164

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Identification Number: 10.1214/17-AAP1308


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.

Item Type: Article
Official URL:
Additional Information: © 2017 Institute of Mathematical Statistics
Divisions: Mathematics
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
Date Deposited: 05 May 2017 09:27
Last Modified: 07 Jun 2024 20:24

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