Outperforming the market portfolio with a given probability

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1465-1494
Journal / PublicationAnnals of Applied Probability
Volume22
Issue number4
Publication statusPublished - Aug 2012

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. © 2012 Institute of Mathematical Statistics.

Research Area(s)

  • Nonuniqueness of solutions of nonlinear PDEs, Optimal arbitrage, Quantile hedging, Strict local martingale deflators, Viscosity solutions

Citation Format(s)

Outperforming the market portfolio with a given probability. / Bayraktar, Erhan; Huang, Yu-Jui; Song, Qingshuo.

In: Annals of Applied Probability, Vol. 22, No. 4, 08.2012, p. 1465-1494.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review