Relative arbitrage: sharp time horizons and motion by curvature. (English) Zbl 1522.91228
Summary: We characterize the minimal time horizon over which any equity market with \(d \geq 2\) stocks and sufficient intrinsic volatility admits relative arbitrage with respect to the market portfolio. If \(d \in \{ 2 , 3 \}\), the minimal time horizon can be computed explicitly, its value being zero if \(d = 2\) and \(\sqrt{3} / ( 2 \pi )\) if \(d = 3\). If \(d \geq 4\), the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in \(\mathbb{R}^d\) that we call the minimum curvature flow.
{© 2021 The Authors. Mathematical Finance published by Wiley Periodicals LLC}
{© 2021 The Authors. Mathematical Finance published by Wiley Periodicals LLC}
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