Outperforming the Market Portfolio with a Given Probability
The Annals of Applied Probability (2012), Vol. 22, No. 4, 1465-1494
30 Pages
Posted: 1 Feb 2014
University of Michigan at Ann Arbor - Department of Mathematics
University of Colorado, Boulder
City University of Hong Kong (CityUHK)
Date Written: June 1, 2011
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.
Keywords: strict local martingale deflators, optimal arbitrage, quantile hedging, viscosity solutions, nonuniqueness of solutions of nonlinear PDEs
Suggested Citation:
Suggested Citation
Bayraktar, Erhan and Huang, Yu-Jui and Song, Qingshuo, Outperforming the Market Portfolio with a Given Probability (June 1, 2011). The Annals of Applied Probability (2012), Vol. 22, No. 4, 1465-1494. Available at SSRN: https://ssrn.com/abstract=2388022
