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. If d ∈ {2, 3}, the minimal time horizon can be computed explicitly, its value being zero if √ d = 2 and 3/(2π) 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.