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      Relative Arbitrage: Sharp Time Horizons and Motion by Curvature

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          Abstract

          We characterize the minimal time horizon over which any market with \(d \geq 2\) stocks and sufficient intrinsic volatility admits relative arbitrage. 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 \(R^d\) that we call the minimum curvature flow.

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          Author and article information

          Journal
          30 March 2020
          Article
          2003.13601
          b4b45074-98c8-4adf-8088-73eb09acba33

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          35J60, 49L25, 60G44, 91G10
          q-fin.MF math.AP math.PR

          Analysis,Probability,Quantitative finance
          Analysis, Probability, Quantitative finance

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