Relative arbitrage: Sharp time horizons and motion by curvature

Martin Larsson and Johannes Ruf

Mathematical Finance, 2021, vol. 31, issue 3, 885-906

Abstract: 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 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 Rd that we call the minimum curvature flow.

Date: 2021
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