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Generalised Lyapunov Functions and Functionally Generated Trading Strategies

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  • Johannes Ruf
  • Kangjianan Xie

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

  • Johannes Ruf & Kangjianan Xie, 2019. "Generalised Lyapunov Functions and Functionally Generated Trading Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(4), pages 293-327, July.
    • Handle: RePEc:taf:apmtfi:v:26:y:2019:i:4:p:293-327
    DOI: 10.1080/1350486X.2019.1584041
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    Citations

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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. 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.
    3. Johannes Ruf & Kangjianan Xie, 2019. "The impact of proportional transaction costs on systematically generated portfolios," Papers 1904.08925, arXiv.org.
    4. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    5. 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.
    6. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.
    7. 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.
    8. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2024. "Quantifying dimensional change in stochastic portfolio theory," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 977-1021, July.
    9. 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.
    10. Donghan Kim, 2023. "Market-to-book ratio in stochastic portfolio theory," Finance and Stochastics, Springer, vol. 27(2), pages 401-434, April.

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