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Evolutionary stable stock markets

Evstigneev, Igor ; Hens, Thorsten ; Schenk-Hoppé, Klaus

In: Economic Theory, 2006, vol. 27, no. 2, p. 449-468

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    Title
    • Evolutionary stable stock markets
    Author
    • Evstigneev, Igor. School of Economic Studies, University of Manchester, Oxford Road, M13 9PL, Manchester, UNITED KINGDOM
    • Hens, Thorsten. Institute for Empirical Research in Economics, University of Zurich, Blümlisalpstrasse 10, 8006, Zürich, SWITZERLAND
    • Schenk-Hoppé, Klaus. Institute for Empirical Research in Economics, University of Zurich, Blümlisalpstrasse 10, 8006, Zürich, SWITZERLAND
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:318832
    Summary
    Summary.: 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)