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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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  • 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.

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File URL: http://arxiv.org/pdf/0909.4730
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Paper provided by arXiv.org in its series Papers with number 0909.4730.

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Date of creation: Sep 2009
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Handle: RePEc:arx:papers:0909.4730

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Web page: http://arxiv.org/

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  1. M A H Dempster & I V Evstigneev & M I Taksar, 2005. "Asset pricing and hedging in financial markets with transaction costs: an approach based on the von Neumann-Gale model," Working Papers 062005, University of Cambridge, Judge Business School, Centre for Financial Research.
  2. 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.
  3. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  4. Garud Iyengar, 2005. "Universal Investment In Markets With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 359-371.
  5. 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.
  6. repec:fth:inseep:9513 is not listed on IDEAS
  7. 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.
  8. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
  9. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
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