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Relative arbitrage: sharp time horizons and motion by curvature

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  • Larsson, Martin
  • Ruf, Johannes

Abstract

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

Suggested Citation

  • Larsson, Martin & Ruf, Johannes, 2021. "Relative arbitrage: sharp time horizons and motion by curvature," LSE Research Online Documents on Economics 108546, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:108546
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    File URL: http://eprints.lse.ac.uk/108546/
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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.

    More about this item

    Keywords

    arbitrage; geometric flow; stochastic control; stochastic portfolio theory;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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