OUTPERFORMING THE MARKET PORTFOLIO WITH A GIVEN PROBABILITY

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Huang, Yu-Jui; Song, Qingshuo
• 署名单位: University of Michigan System; University of Michigan; City University of Hong Kong
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP799
• 发表日期: 2012
• 页码: 1465-1494
• 关键词: ASSET PRICE BUBBLES; local martingales; arbitrage

摘要

Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do not assume the existence of an equivalent local martingale measure, but merely the existence of a local martingale deflator.