Outperforming the Market Portfolio with a Given Probability

Details Outperforming the Market Portfolio with a Given Probability Outperforming the Market Portfolio with a Given Probability

2010-06-13

arxiv.org/abs/1006.3224v5

Economy

Quantitative Finance

Computational Finance

Keywords: Strict local martingales deflators, optimal arbitrage, quantile hedging, viscosity solutions, nonuniqueness of solut

Scientific paper

Our goal is to resolve a problem proposed by Karatzas and Fernholz (2008): Characterizing the minimum amount of initial capital that would guarantee the investor to 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 supersolution of a non-linear PDE. As in Karatzas and Fernholz (2008), 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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