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Globally evolutionarily stable portfolio rules

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

Abstract

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 rule of "betting your beliefs." A game theoretic interpretation of this result is given.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:197-228
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    References listed on IDEAS

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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.
    2. J. Doyne Farmer & Andrew W. Lo, 1999. "Frontiers of Finance: Evolution and Efficient Markets," Working Papers 99-06-039, Santa Fe Institute.
    3. Arthur, W.B. & Holland, J.H. & LeBaron, B. & Palmer, R. & Tayler, P., 1996. "Asset Pricing Under Endogenous Expectations in an Artificial Stock Market," Working papers 9625, Wisconsin Madison - Social Systems.
    4. 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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    6. Schlicht, Ekkehart, . "Isolation and Aggregation in Economics," Monographs in Economics, University of Munich, Department of Economics, number 38821, November.
    7. Alos-Ferrer, Carlos & Ania, Ana B., 2005. "The asset market game," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 67-90, February.
    8. Dempster, M. A. H. & Germano, M. & Medova, E. A. & Villaverde, M., 2003. "Global Asset Liability Management," British Actuarial Journal, Cambridge University Press, vol. 9(01), pages 137-195, April.
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    10. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
    11. 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.
    12. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, 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. repec:spr:compst:v:73:y:2011:i:2:p:235-250 is not listed on IDEAS
    5. Anufriev, Mikhail & Bottazzi, Giulio, 2010. "Market equilibria under procedural rationality," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1140-1172, November.
    6. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2018. "Momentum and Reversal in Financial Markets with Persistent Heterogeneity," LEM Papers Series 2018/04, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    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. "Market selection of constant proportions investment strategies in continuous time," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 248-266, March.
    14. 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.

    More about this item

    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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