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Relative Arbitrage: Sharp Time Horizons and Motion by Curvature

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  • Martin Larsson
  • Johannes Ruf

Abstract

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.

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  • Martin Larsson & Johannes Ruf, 2020. "Relative Arbitrage: Sharp Time Horizons and Motion by Curvature," Papers 2003.13601, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2003.13601
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    References listed on IDEAS

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    1. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, arXiv.org.
    2. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
    3. Pal, Soumik, 2019. "Exponentially concave functions and high dimensional stochastic portfolio theory," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3116-3128.
    4. E. Robert Fernholz & Ioannis Karatzas & Johannes Ruf, 2016. "Volatility and Arbitrage," Papers 1608.06121, arXiv.org.
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    Cited by:

    1. David Itkin & Benedikt Koch & Martin Larsson & Josef Teichmann, 2022. "Ergodic robust maximization of asymptotic growth under stochastic volatility," Papers 2211.15628, arXiv.org.
    2. Cox, Alexander M.G. & Robinson, Benjamin A., 2023. "Optimal control of martingales in a radially symmetric environment," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 149-198.
    3. David Itkin & Martin Larsson, 2024. "Calibrated rank volatility stabilized models for large equity markets," Papers 2403.04674, arXiv.org.

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