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Evolutionary stable stock markets

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  • Igor Evstigneev

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  • Thorsten Hens

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  • Klaus Schenk-Hoppé

    ()

Abstract

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

Suggested Citation

  • Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
  • Handle: RePEc:spr:joecth:v:27:y:2006:i:2:p:449-468 DOI: 10.1007/s00199-005-0607-8
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    References listed on IDEAS

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    1. Murata, Yasuo, 1977. "Mathematics for Stability and Optimization of Economic Systems," Elsevier Monographs, Elsevier, edition 1, number 9780125112505 edited by Shell, Karl.
    2. Klaus Reiner Schenk-Hopp�, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
    3. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    4. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 74(4), pages 929-966, July.
    5. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095.
    6. 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.
    7. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
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    Citations

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    Cited by:

    1. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner & Wang, Tongya, 2016. "Itchy feet vs cool heads: Flow of funds in an agent-based financial market," Journal of Economic Dynamics and Control, Elsevier, vol. 63(C), pages 53-68.
    2. De Giorgi, Enrico, 2008. "Evolutionary portfolio selection with liquidity shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1088-1119, April.
    3. repec:spr:compst:v:73:y:2011:i:2:p:235-250 is not listed on IDEAS
    4. Gerber, Anke & Hens, Thorsten & Woehrmann, Peter, 2005. "Dynamic General Equilibrium and T-Period Fund Separation," Discussion Papers 2005/16, Norwegian School of Economics, Department of Business and Management Science.
    5. Anufriev, Mikhail & Bottazzi, Giulio, 2010. "Market equilibria under procedural rationality," Journal of Mathematical Economics, Elsevier, pages 1140-1172.
    6. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
    7. LeBaron, Blake, 2012. "Heterogeneous gain learning and the dynamics of asset prices," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 424-445.
    8. Bruno S. Frey & Simon Luechinger & Alois Stutzer, 2007. "Calculating Tragedy: Assessing The Costs Of Terrorism," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 1-24, February.
    9. Anufriev, Mikhail & Dindo, Pietro, 2010. "Wealth-driven selection in a financial market with heterogeneous agents," Journal of Economic Behavior & Organization, Elsevier, vol. 73(3), pages 327-358, March.
    10. Saroj Bhattarai & Gauti B. Eggertsson & Raphael Schoenle, 2012. "Is increased price flexibility stabilizing? Redux," Staff Reports 540, Federal Reserve Bank of New York.
    11. W. Bahsoun & I. Evstigneev & L. Xu, 2011. "Almost sure Nash equilibrium strategies in evolutionary models of asset markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 235-250, April.
    12. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "From discrete to continuous time evolutionary finance models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 913-931, May.
    13. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "Market selection of constant proportions investment strategies in continuous time," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 248-266, March.
    14. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner, 2006. "On the Evolution of Investment Strategies and the Kelly Rule – A Darwinian Approach," Discussion Papers 2006/23, Norwegian School of Economics, Department of Business and Management Science.
    15. Evstigneev, Igor V. & Hens, Thorsten & Schenk-Hoppé, Klaus Reiner, 2008. "Globally evolutionarily stable portfolio rules," Journal of Economic Theory, Elsevier, vol. 140(1), pages 197-228, May.
    16. Thorsten Hens & Terje Lensberg & Klaus Schenk-Hoppé & Peter Wöhrmann, 2011. "An evolutionary explanation of the value premium puzzle," Journal of Evolutionary Economics, Springer, pages 803-815.

    More about this item

    Keywords

    Evolutionary finance; Portfolio theory; Incomplete markets.;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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