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arXiv · 1006.3224

Outperforming the market portfolio with a given probability

Erhan Bayraktar·Yu-Jui Huang·Qingshuo Song
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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.

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Erhan Bayraktar, Yu-Jui Huang, Qingshuo Song. 2010-06-13. Outperforming the market portfolio with a given probability. https://doi.org/10.1214/11-aap799

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