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An evolutionary financial market model with a risk-free asset

Author

Listed:
  • Igor V. EVSTIGNEEVY

    (University of Manchester)

  • Thorsten HENS

    (University of Zurich and Swiss Finance Institute)

  • Klaus Reiner SCHENK-HOPPE

    (University of Leeds)

Abstract

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. We focus on the local stability of the wealth dynamics, applying recent results on the linearization and stability of random dynamical systems (Evstigneev, Pirogov and Schenk-Hoppé (Proceedings of the American Mathematical Society, forthcoming). Our results give conditions on the linearization of the model at an equilibrium state, ensuring local convergence of sample paths to this equilibrium. The concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy is derived.

Suggested Citation

  • Igor V. EVSTIGNEEVY & Thorsten HENS & Klaus Reiner SCHENK-HOPPE, "undated". "An evolutionary financial market model with a risk-free asset," Swiss Finance Institute Research Paper Series 10-36, Swiss Finance Institute.
  • Handle: RePEc:chf:rpseri:rp1036
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    References listed on IDEAS

    as
    1. 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.
    2. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. 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.
    4. Terje Lensberg & Klaus Reiner Schenk-Hoppe, 2006. "On the Evolution of Investment Strategies and the Kelly Rule – A Darwinian Approach," Swiss Finance Institute Research Paper Series 06-38, Swiss Finance Institute.
    5. 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.
    6. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2006. "Markets do not select for a liquidity preference as behavior towards risk," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 279-292, February.
    7. Thorsten Hens & Terje Lensberg & Klaus Schenk-Hoppé & Peter Wöhrmann, 2011. "An evolutionary explanation of the value premium puzzle," Journal of Evolutionary Economics, Springer, vol. 21(5), pages 803-815, December.
    8. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    9. Thorsten Hens & Klaus Reiner Schenk-Hoppé & Martin Stalder, 2002. "An Application of Evolutionary Finance to Firms Listed in the Swiss Market Index," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 138(IV), pages 465-487, December.
    10. Chiarella, Carl & He, Xue-Zhong & Zheng, Min, 2011. "An analysis of the effect of noise in a heterogeneous agent financial market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 148-162, January.
    11. Jean-Jacques Laffont, 1989. "The Economics of Uncertainty and Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121360, January.
    12. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
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    More about this item

    Keywords

    Evolutionary finance; risk-free asset; local stability.;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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