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Generalised Lyapunov functions and functionally generated trading strategies

Author

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  • 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. "Generalised Lyapunov functions and functionally generated trading strategies," LSE Research Online Documents on Economics 102424, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:102424
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    File URL: http://eprints.lse.ac.uk/102424/
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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. 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.
    3. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Working Papers hal-01349639, HAL.
    4. Adrian Banner & Robert Fernholz & Vassilios Papathanakos & Johannes Ruf & David Schofield, 2018. "Diversification, Volatility, and Surprising Alpha," Papers 1809.03769, arXiv.org.
    5. Winslow Strong, 2012. "Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage," Papers 1212.1877, arXiv.org, revised Oct 2013.
    6. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    7. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    8. Ting-Kam Leonard Wong, 2017. "On portfolios generated by optimal transport," Papers 1709.03169, arXiv.org, revised Sep 2017.
    9. 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.
    10. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Abi Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Post-Print hal-01349639, HAL.
    11. Robert Fernholz, 1999. "Portfolio Generating Functions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 15, pages 344-367, World Scientific Publishing Co. Pte. Ltd..
    12. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Prömel, 2023. "Model‐free portfolio theory: A rough path approach," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 709-765, July.
    2. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2023. "Quantifying dimensional change in stochastic portfolio theory," Papers 2303.00858, arXiv.org, revised Apr 2023.
    3. David Itkin & Benedikt Koch & Martin Larsson & Josef Teichmann, 2022. "Ergodic robust maximization of asymptotic growth under stochastic volatility," Papers 2211.15628, arXiv.org.
    4. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Promel, 2021. "Model-free Portfolio Theory: A Rough Path Approach," Papers 2109.01843, arXiv.org, revised Oct 2022.
    5. Johannes Ruf & Kangjianan Xie, 2019. "The impact of proportional transaction costs on systematically generated portfolios," Papers 1904.08925, arXiv.org.
    6. Ruf, Johannes & Xie, Kangjianan, 2020. "Impact of proportional transaction costs on systematically generated portfolios," LSE Research Online Documents on Economics 104696, London School of Economics and Political Science, LSE Library.
    7. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    8. Donghan Kim, 2023. "Market-to-book ratio in stochastic portfolio theory," Finance and Stochastics, Springer, vol. 27(2), pages 401-434, April.
    9. Ioannis Karatzas & Donghan Kim, 2020. "Trading strategies generated pathwise by functions of market weights," Finance and Stochastics, Springer, vol. 24(2), pages 423-463, April.
    10. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.

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    More about this item

    Keywords

    Additive generation; Lyapunov function; market diversity; multi- plicative 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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