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Growth-optimal investments and numeraire portfolios under transaction costs: An analysis based on the von Neumann-Gale model

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Listed:
  • Wael Bahsoun
  • Igor V. Evstigneev
  • Michael I. Taksar

Abstract

The aim of this work is to extend the capital growth theory developed by Kelly, Breiman, Cover and others to asset market models with transaction costs. We define a natural generalization of the notion of a numeraire portfolio proposed by Long and show how such portfolios can be used for constructing growth-optimal investment strategies. The analysis is based on the classical von Neumann-Gale model of economic dynamics, a stochastic version of which we use as a framework for the modelling of financial markets with frictions.

Suggested Citation

  • Wael Bahsoun & Igor V. Evstigneev & Michael I. Taksar, 2009. "Growth-optimal investments and numeraire portfolios under transaction costs: An analysis based on the von Neumann-Gale model," Papers 0909.4730, arXiv.org.
  • Handle: RePEc:arx:papers:0909.4730
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    File URL: http://arxiv.org/pdf/0909.4730
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/5630 is not listed on IDEAS
    2. repec:crs:wpaper:9513 is not listed on IDEAS
    3. Garud Iyengar, 2005. "Universal Investment In Markets With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 359-371.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    5. repec:jbs:wpaper:062005 is not listed on IDEAS
    6. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    7. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    8. Evstigneev, Igor V. & Schenk-Hoppe, Klaus Reiner, 2007. "Pure and randomized equilibria in the stochastic von Neumann-Gale model," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 871-887, September.
    9. Wael Bahsoun & Igor Evstigneev & Michael Taksar, 2007. "Rapid paths in von Neumann-Gale dynamical systems," The School of Economics Discussion Paper Series 0718, Economics, The University of Manchester.
    10. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
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