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Generalized Lyapunov functions and functionally generated trading strategies

Author

Listed:
  • Ruf, Johannes
  • Xie, Kangjianan

Abstract

This paper investigates the dependence of functional portfolio generation, introduced by Fernholz (1999), on an extra finite variation process. The framework of Karatzas and Ruf (2017) is used to formulate conditions on trading strategies to be strong arbitrage relative to the market over sufficiently large time horizons. A mollification argument and Komlós theorem yield a general class of potential arbitrage strategies. These theoretical results are complemented by several empirical examples using data from the S&P 500 stocks.

Suggested Citation

  • Ruf, Johannes & Xie, Kangjianan, 2019. "Generalized Lyapunov functions and functionally generated trading strategies," LSE Research Online Documents on Economics 100023, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:100023
    as

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    File URL: http://eprints.lse.ac.uk/100023/
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    References listed on IDEAS

    as
    1. Banner, Adrian D. & Ghomrasni, Raouf, 2008. "Local times of ranked continuous semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1244-1253, July.
    2. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    3. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    4. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    5. Adrian Banner & Robert Fernholz & Vassilios Papathanakos & Johannes Ruf & David Schofield, 2018. "Diversification, Volatility, and Surprising Alpha," Papers 1809.03769, arXiv.org.
    6. Ting-Kam Leonard Wong, 2017. "On portfolios generated by optimal transport," Papers 1709.03169, arXiv.org, revised Sep 2017.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    additive generation; Lyapunov function; market diversity; multiplicative generation; portfolio analysis; portfolio generating function; regular function; S&P 500; Stochastic Portfolio Theory;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance
    • J1 - Labor and Demographic Economics - - Demographic Economics

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