Outperforming the market portfolio with a given probability
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.
Cite
@article{arxiv.1006.3224,
title = {Outperforming the market portfolio with a given probability},
author = {Erhan Bayraktar and Yu-Jui Huang and Qingshuo Song},
journal= {arXiv preprint arXiv:1006.3224},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP799 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)