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).
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Received: 7 October 2003, Revised: 18 January 2005,
JEL Classification Numbers:
G11, D52, D81.
Correspondence to: Klaus Reiner Schenk-Hoppé
We are grateful to Jarrod Wilcox and William Ziemba for valuable comments. Financial support by the national center of competence in research “Financial Valuation and Risk Management” is gratefully acknowledged. The national centers in research are managed by the Swiss National Science Foundation on behalf of the federal authorities.
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Evstigneev, I.V., Hens, T. & Schenk-Hoppé, K.R. Evolutionary stable stock markets. Economic Theory 27, 449–468 (2006). https://doi.org/10.1007/s00199-005-0607-8
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DOI: https://doi.org/10.1007/s00199-005-0607-8