Relative arbitrage: Sharp time horizons and motion by curvature

We characterize the minimal time horizon over which any equity market with d ≥ 2 stocks and sufficient intrinsic volatility admits relative arbitrage with respect to the market portfolio. If d ∈ { 2 , 3 } , the minimal time horizon can be computed explicitly, its value being zero if d = 2 and3 / ( 2 π )if d = 3 . If d ≥ 4 , the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in R d that we call the minimum curvature flow.