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Fractional Kelly Strategies in Continuous Time: Recent Developments

In: HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II

Author

Listed:
  • Mark Davis
  • Sébastien Lleo

Abstract

The Kelly criterion and fractional Kelly strategies hold an important place in investment management theory and practice. Both the Kelly criterion and fractional Kelly strategies, e.g. invest a fraction f of one's wealth in the Kelly portfolio and a proportion 1 − f in the risk-free asset, are optimal in the continuous time setting of the Merton [33] model. However, fractional Kelly strategies are no longer optimal when the basic assumptions of the Merton model, such as the lognormality of asset prices, are removed. In this chapter, we present an overview of some recent developments related to Kelly investment strategies in an incomplete market environment where asset prices are not lognormally distributed. We show how the definition of fractional Kelly strategies can be extended to guarantee optimality. The key idea is to get the definition of fractional Kelly strategies to coincide with the fund separation theorem related to the problem at hand. In these instances, fractional Kelly investment strategies appear as the natural solution for investors seeking to maximize the terminal power utility of their wealth.

Suggested Citation

  • Mark Davis & Sébastien Lleo, 2013. "Fractional Kelly Strategies in Continuous Time: Recent Developments," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 37, pages 753-787, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814417358_0037
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    Citations

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    Cited by:

    1. Bermin, Hans-Peter & Holm, Magnus, 2021. "Leverage and risk relativity: how to beat an index," Knut Wicksell Working Paper Series 2021/1, Lund University, Knut Wicksell Centre for Financial Studies.
    2. Jan Obłój & Thaleia Zariphopoulou, 2021. "In memoriam: Mark H. A. Davis and his contributions to mathematical finance," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1099-1110, October.
    3. Hans‐Peter Bermin & Magnus Holm, 2021. "Kelly trading and option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(7), pages 987-1006, July.
    4. Jan-Christian Gerlach & Jerome Kreuser & Didier Sornette, 2020. "Awareness of crash risk improves Kelly strategies in simulated financial time series," Papers 2004.09368, arXiv.org.

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