Financial/Actuarial Mathematics Seminar

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 largest subsolution of a nonlinear 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.
Joint work with Erhan Bayraktar and Qinghuo Song. Available at http://arxiv.org/abs/1006.3224