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Globally Evolutionarily Stable Portfolio Rules

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The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. Assets pay dividends, that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify globally evolutionarily stable strategies, allowing an investor to “survive,” i.e., to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this property—an analogue of the famous Kelly (1956) rule of “betting one’s beliefs.”

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  • Evstigneev, Igor V. & Hens, Thorsten & Schenk-Hoppé, Klaus Reiner, 2005. "Globally Evolutionarily Stable Portfolio Rules," Discussion Papers 2005/17, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2005_017
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    1. Amir, Rabah & Evstigneev, Igor V. & Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Market selection and survival of investment strategies," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 105-122, February.
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    12. 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.
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    Cited by:

    1. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner & Wang, Tongya, 2016. "Itchy feet vs cool heads: Flow of funds in an agent-based financial market," Journal of Economic Dynamics and Control, Elsevier, vol. 63(C), pages 53-68.
    2. LeBaron, Blake, 2012. "Wealth dynamics and a bias toward momentum trading," Finance Research Letters, Elsevier, vol. 9(1), pages 21-28.
    3. Bottazzi, Giulio & Dindo, Pietro, 2014. "Evolution and market behavior with endogenous investment rules," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 121-146.
    4. Guillaume Coqueret & Bertrand Tavin, 2019. "Procedural rationality, asset heterogeneity and market selection," Post-Print hal-02312310, HAL.
    5. Anufriev, Mikhail & Bottazzi, Giulio, 2010. "Market equilibria under procedural rationality," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1140-1172, November.
    6. Rabah Amir & Igor Evstigneev & Klaus Schenk-Hoppé, 2013. "Asset market games of survival: a synthesis of evolutionary and dynamic games," Annals of Finance, Springer, vol. 9(2), pages 121-144, May.
    7. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
    8. Çisem Bektur, 2013. "Performance of investment strategies in the absence of correct beliefs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(1), pages 23-37, May.
    9. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2018. "Long-run heterogeneity in an exchange economy with fixed-mix traders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 407-447, August.
    10. Giulio Bottazzi & Pietro Dindo, 2013. "Selection in asset markets: the good, the bad, and the unknown," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 641-661, July.
    11. Hommes, C.H. & Wagener, F.O.O., 2008. "Complex evolutionary systems in behavioral finance," CeNDEF Working Papers 08-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    12. 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.
    13. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "From discrete to continuous time evolutionary finance models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 913-931, May.
    14. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "Market selection of constant proportions investment strategies in continuous time," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 248-266, March.
    15. Serena Brianzoni & Cristiana Mammana & Elisabetta Michetti, 2010. "Updating Wealth in an Asset Pricing Model with Heterogeneous Agents," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-27, November.
    16. Hirshleifer, David & Lo, Andrew W. & Zhang, Ruixun, 2023. "Social contagion and the survival of diverse investment styles," Journal of Economic Dynamics and Control, Elsevier, vol. 154(C).
    17. Igor V. EVSTIGNEEVY & Thorsten HENS & Klaus Reiner SCHENK-HOPPE, 2010. "An evolutionary financial market model with a risk-free asset," Swiss Finance Institute Research Paper Series 10-36, Swiss Finance Institute.
    18. Thomas Holtfort, 2019. "From standard to evolutionary finance: a literature survey," Management Review Quarterly, Springer, vol. 69(2), pages 207-232, June.
    19. 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.
    20. Rabah Amir & Igor V. Evstigneev & Valeriya Potapova, 2021. "Unbeatable Strategies," Economics Discussion Paper Series 2101, Economics, The University of Manchester, revised Jul 2023.
    21. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2019. "Momentum and reversal in financial markets with persistent heterogeneity," Annals of Finance, Springer, vol. 15(4), pages 455-487, December.
    22. Daniele Giachini, 2021. "Rationality and asset prices under belief heterogeneity," Journal of Evolutionary Economics, Springer, vol. 31(1), pages 207-233, January.
    23. Coqueret, Guillaume & Tavin, Bertrand, 2019. "Procedural rationality, asset heterogeneity and market selection," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 125-149.
    24. I. V. Evstigneev & T. Hens & M. J. Vanaei, 2023. "Evolutionary finance: a model with endogenous asset payoffs," Journal of Bioeconomics, Springer, vol. 25(2), pages 117-143, August.

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    More about this item

    Keywords

    Evolutionary Finance; Wealth Dynamics; Survival and Extinction of Portfolio Rules; Evolutionary Stability; Kelly Rule;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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