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Almost sure Nash equilibrium strategies in evolutionary models of asset markets

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  • W. Bahsoun
  • I. Evstigneev
  • L. Xu

Abstract

We consider a stochastic model of a financial market with long-lived dividend-paying assets and endogenous asset prices. The model was initially developed and analyzed in the context of evolutionary finance, with the main focus on questions of “survival and extinction” of investment strategies. In this paper we view the model from a different, game-theoretic, perspective and examine Nash equilibrium strategies, satisfying equilibrium conditions with probability one. Copyright Springer-Verlag 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:73:y:2011:i:2:p:235-250
    DOI: 10.1007/s00186-010-0344-z
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    References listed on IDEAS

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    1. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner (ed.), 2009. "Handbook of Financial Markets: Dynamics and Evolution," Elsevier Monographs, Elsevier, edition 1, number 9780123742582.
    2. 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.
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    4. 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, October.
    5. Robert Bell & Thomas M. Cover, 1988. "Game-Theoretic Optimal Portfolios," Management Science, INFORMS, vol. 34(6), pages 724-733, June.
    6. Daniel Kuhn & David Luenberger, 2010. "Analysis of the rebalancing frequency in log-optimal portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 221-234.
    7. Rabah AMIR & Igor V. EVSTIGNEEV & Thorsten HENS & Le XU, 2009. "Evolutionary Finance and Dynamic Games," Swiss Finance Institute Research Paper Series 09-49, Swiss Finance Institute.
    8. 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.
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    Cited by:

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