Relative arbitrage: Sharp time horizons and motion by curvature

Abstract

We characterize the minimal time horizon over which any equity market with (Formula presented.) stocks and sufficient intrinsic volatility admits relative arbitrage with respect to the market portfolio. If (Formula presented.), the minimal time horizon can be computed explicitly, its value being zero if (Formula presented.) and (Formula presented.) if (Formula presented.). If (Formula presented.), the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in (Formula presented.) that we call the minimum curvature flow.