Open Access
August 2012 Outperforming the market portfolio with a given probability
Erhan Bayraktar, Yu-Jui Huang, Qingshuo Song
Ann. Appl. Probab. 22(4): 1465-1494 (August 2012). DOI: 10.1214/11-AAP799


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.


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Erhan Bayraktar. Yu-Jui Huang. Qingshuo Song. "Outperforming the market portfolio with a given probability." Ann. Appl. Probab. 22 (4) 1465 - 1494, August 2012.


Published: August 2012
First available in Project Euclid: 10 August 2012

zbMATH: 1259.60072
MathSciNet: MR2985167
Digital Object Identifier: 10.1214/11-AAP799

Primary: 60H10 , 60H30 , 91G99
Secondary: 35A02 , 60G44 , 60J70

Keywords: nonuniqueness of solutions of nonlinear PDEs , optimal arbitrage , quantile hedging , Strict local martingale deflators , viscosity solutions

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 4 • August 2012
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