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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≥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.

Suggested Citation

  • Martin Larsson & Johannes Ruf, 2021. "Relative arbitrage: Sharp time horizons and motion by curvature," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 885-906, July.
    • Handle: RePEc:bla:mathfi:v:31:y:2021:i:3:p:885-906
    DOI: 10.1111/mafi.12303
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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. Karatzas, Ioannis & Ruf, Johannes, 2017. "Trading strategies generated by Lyapunov functions," LSE Research Online Documents on Economics 69177, London School of Economics and Political Science, LSE Library.
    3. 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.
    4. Fernholz, E. Robert & Karatzas, Ioannis & Ruf, Johannes, 2018. "Volatility and arbitrage," LSE Research Online Documents on Economics 75234, London School of Economics and Political Science, LSE Library.
    5. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    6. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
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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. David Itkin & Martin Larsson, 2024. "Calibrated rank volatility stabilized models for large equity markets," Papers 2403.04674, arXiv.org.
    3. 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.

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