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Evolutionary stable stock markets

  • Igor Evstigneev

    ()

  • Thorsten Hens

    ()

  • Klaus Schenk-Hoppé

    ()

This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded in the sense that there is a portfolio rule that, when introduced on the market with arbitrarily small initial wealth, increases its market share at the incumbent’s expense. This mutant portfolio rule changes the asset valuation in the course of time. The stochastic wealth dynamics in our evolutionary stock market model is formulated as a random dynamical system. Applying this theory, necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when relative dividend payoffs follow a stationary Markov process. These local stability conditions lead to a unique evolutionary stable portfolio rule according to which assets are evaluated by expected relative dividends (with respect to the objective probabilities). Copyright Springer-Verlag Berlin/Heidelberg 2006

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File URL: http://hdl.handle.net/10.1007/s00199-005-0607-8
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Article provided by Springer in its journal Economic Theory.

Volume (Year): 27 (2006)
Issue (Month): 2 (January)
Pages: 449-468

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Handle: RePEc:spr:joecth:v:27:y:2006:i:2:p:449-468
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  1. De Long, J. Bradford & Shleifer, Andrei & Summers, Lawrence H. & Waldmann, Robert J., 1990. "Noise Trader Risk in Financial Markets," Scholarly Articles 3725552, Harvard University Department of Economics.
  2. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
  3. Lawrence Blume & David Easley, 2001. "If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Working Papers 01-06-031, Santa Fe Institute.
  4. Klaus Reiner Schenk-Hoppé, . "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
  5. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2002. "Market Selection Of Financial Trading Strategies: Global Stability," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 329-339.
  6. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095.
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