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Trading strategies generated by Lyapunov functions

Author

Listed:
  • Ioannis Karatzas

    (Columbia University
    Intech Investment Management)

  • Johannes Ruf

    (London School of Economics and Political Science)

Abstract

Functional portfolio generation, initiated by E.R. Fernholz almost 20 years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation structure of the underlying market, and needs no estimation of model parameters. In this paper, the corresponding generating functions G $G$ are interpreted as Lyapunov functions for the vector process μ $\mu $ of relative market weights; that is, via the property that the process G ( μ ) $G (\mu )$ is a supermartingale under an appropriate change of measure. This point of view unifies, generalizes, and simplifies many existing results, and allows the formulation of conditions under which it is possible to outperform the market portfolio over appropriate time horizons. From a probabilistic point of view, the approach offered here yields results concerning the interplay of stochastic discount factors and concave transformations of semimartingales on compact domains.

Suggested Citation

  • Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:3:d:10.1007_s00780-017-0332-8
    DOI: 10.1007/s00780-017-0332-8
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    References listed on IDEAS

    as
    1. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-Weighted Portfolios with Negative Parameter," Papers 1504.01026, arXiv.org, revised Jul 2015.
    2. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    3. 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.
    4. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    5. 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..
    6. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    7. Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.
    8. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    9. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    10. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-weighted portfolios with negative parameter," Annals of Finance, Springer, vol. 11(3), pages 411-432, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Stochastic portfolio theory; Functional generation; Relative arbitrage; Regular and Lyapunov functions; Concavity; Semimartingale property; Deflators;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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