Outperforming the market portfolio with a given probability

Erhan Bayraktar, Yu-Jui Huang and Qingshuo Song

Papers from arXiv.org

Abstract: 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.

Date: 2010-06, Revised 2012-08
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Citations: View citations in EconPapers (9)

Published in Annals of Applied Probability 2012, Vol. 22, No. 4, 1465-1494

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1006.3224

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