Economic Theory

, Volume 27, Issue 2, pp 449–468

Evolutionary stable stock markets

  • Igor V. Evstigneev
  • Thorsten Hens
  • Klaus Reiner Schenk-Hoppé
Research Articles

DOI: 10.1007/s00199-005-0607-8

Cite this article as:
Evstigneev, I.V., Hens, T. & Schenk-Hoppé, K.R. Economic Theory (2006) 27: 449. doi:10.1007/s00199-005-0607-8

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).

Keywords and Phrases:

Evolutionary finance Portfolio theory Incomplete markets. 

Copyright information

© Springer-Verlag Berlin/Heidelberg 2006

Authors and Affiliations

  • Igor V. Evstigneev
    • 1
  • Thorsten Hens
    • 2
  • Klaus Reiner Schenk-Hoppé
    • 2
    • 3
  1. 1.School of Economic StudiesUniversity of ManchesterManchesterUNITED KINGDOM
  2. 2.Institute for Empirical Research in EconomicsUniversity of ZurichZürichSWITZERLAND
  3. 3.Leeds University Business School and School of MathematicsUniversity of LeedsLeedsUNITED KINGDOM

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