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Trading strategies generated by Lyapunov functions

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  • Karatzas, Ioannis
  • Ruf, Johannes

Abstract

Functional portfolio generation, initiated by E.R. Fernholz almost twenty 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 model, and needs no estimation of model parameters. In this paper, the corresponding generating functions G are interpreted as Lyapunov functions for the vector process μ(⋅) of market weights; that is, via the property that G(μ(⋅)) is a supermartingale under an appropriate change of measure. This point of view unifies, generalizes, and simplifies several 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 present paper yields results concerning the interplay of stochastic discount factors and concave transformations of semimartingales on compact domains.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:69177
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    File URL: http://eprints.lse.ac.uk/69177/
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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. 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..
    3. 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)

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    More about this item

    Keywords

    trading strategies; functional generation; relative arbitrage; regular and Lyapunov functions; concavity; semimartingale property; deflators;
    All these keywords.

    JEL classification:

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

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