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Evolutionary stability of portfolio rules in incomplete markets

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  • Hens, Thorsten
  • Schenk-Hoppe, Klaus Reiner

Abstract

This paper studies the evolution of market shares of portfolio rules in incomplete markets with short-lived assets. Prices are determined endogenously. The performance of a portfolio rule in the process of continuous reinvestment of wealth is determined by the market share eventually conquered in competition with other portfolio rules. Using random dynamical systems theory, we derive necessary and sufficient conditions for the evolutionary stability of portfolio rules. In the case of Markov (in particular i.i.d.) payoffs these local stability conditions lead to a simple portfolio rule that is the unique evolutionary stable strategy. This rule possesses an explicit representation. Moreover, it is demonstrated that mean-variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 41 (2005)
Issue (Month): 1-2 (February)
Pages: 43-66

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Handle: RePEc:eee:mateco:v:41:y:2005:i:1-2:p:43-66

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Web page: http://www.elsevier.com/locate/jmateco

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  1. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, . "Market Selection of Financial Trading Strategies: Global Stability," IEW - Working Papers 083, Institute for Empirical Research in Economics - University of Zurich.
  2. Sciubba, E., 1999. "The Evolution of Portfolio Rules and the Capital Asset Pricing Model," Cambridge Working Papers in Economics 9909, Faculty of Economics, University of Cambridge.
  3. Klaus Reiner Schenk-Hoppé, . "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
  4. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
  5. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  6. J. Doyne Farmer & Andrew W. Lo, 1999. "Frontiers of Finance: Evolution and Efficient Markets," Working Papers 99-06-039, Santa Fe Institute.
  7. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
  8. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29.
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