VOLATILITY AND ARBITRAGE

• 成果类型: Article
• 署名作者: Fernholz, E. Robert; Karatzas, Ioannis; Ruf, Johannes
• 署名单位: Columbia University; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1308
• 发表日期: 2018
• 页码: 378-417
• 关键词: relative arbitrage; numeraire

摘要

in an equity market consisting of a fixed number d of assets with capitalization weights mu(i) (.), 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.