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

Benjamin Jourdain () and Julien Reygner ()
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Benjamin Jourdain: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk handling - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées
Julien Reygner: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Stochastic Portfolio Theory; Capital distribution curves; Rank-based models; Mean-field Atlas model; Growth rate; Size effect (search for similar items in EconPapers)
Date: 2015-05
Note: View the original document on HAL open archive server: https://enpc.hal.science/hal-00921151v3
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Citations: View citations in EconPapers (3)

Published in Annals of Finance, 2015, 11 (2), pp.151-198. ⟨10.1007/s10436-014-0258-5⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00921151

DOI: 10.1007/s10436-014-0258-5

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