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

Benjamin Jourdain 1, 2 Julien Reygner 1, 3, *
* Corresponding author
2 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
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.
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https://hal-enpc.archives-ouvertes.fr/hal-00921151
Contributor : Julien Reygner <>
Submitted on : Sunday, November 2, 2014 - 10:30:48 PM
Last modification on : Friday, March 27, 2020 - 2:55:49 AM
Document(s) archivé(s) le : Tuesday, February 3, 2015 - 10:15:25 AM

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Benjamin Jourdain, Julien Reygner. Capital distribution and portfolio performance in the mean-field Atlas model. Annals of Finance, Springer Verlag, 2015, 11 (2), pp.151-198. ⟨10.1007/s10436-014-0258-5⟩. ⟨hal-00921151v3⟩

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