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Capital distribution and portfolio performance in the mean-field Atlas model

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  • Benjamin Jourdain
  • Julien Reygner

Abstract

We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of stochastic portfolio theory. We obtain an asymptotic description of the market when the number of companies grows to infinity. Then, we discuss the long-term capital distribution. We recover the Pareto-like shape of capital distribution curves usually derived from empirical studies, and provide a new description of the phase transition phenomenon observed by Chatterjee and Pal. Finally, we address the performance of simple portfolio rules and highlight the influence of the volatility structure on the growth of portfolios. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Annals of Finance, Springer, vol. 11(2), pages 151-198, May.
    • Handle: RePEc:kap:annfin:v:11:y:2015:i:2:p:151-198
    DOI: 10.1007/s10436-014-0258-5
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    References listed on IDEAS

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    1. Shkolnikov, Mykhaylo, 2012. "Large systems of diffusions interacting through their ranks," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1730-1747.
    2. Shkolnikov, Mykhaylo, 2013. "Large volatility-stabilized markets," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 212-228.
    3. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Andrey Sarantsev, 2019. "Comparison Techniques for Competing Brownian Particles," Journal of Theoretical Probability, Springer, vol. 32(2), pages 545-585, June.
    2. Sergio A. Almada Monter & Mykhaylo Shkolnikov & Jiacheng Zhang, 2018. "Dynamics of observables in rank-based models and performance of functionally generated portfolios," Papers 1802.03593, arXiv.org.
    3. Brandon Flores & Blessing Ofori-Atta & Andrey Sarantsev, 2021. "A stock market model based on CAPM and market size," Annals of Finance, Springer, vol. 17(3), pages 405-424, September.

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    More about this item

    Keywords

    Stochastic portfolio theory; Capital distribution curves; Rank-based models; Mean-field Atlas model; Growth rate; Size effect; G10; G11;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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