%0 Unpublished work %T Capital distribution and portfolio performance in the mean-field Atlas model %+ Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) %+ Mathematical Risk handling (MATHRISK) %+ Laboratoire de Probabilités et Modèles Aléatoires (LPMA) %A Jourdain, Benjamin %A Reygner, Julien %Z Chaire Risques Financiers, Fondation du Risque %8 2014-08-20 %D 2014 %Z 1312.5660 %K Stochastic Portfolio Theory %K Capital distribution curves %K Rank-based models %K Mean-field Atlas model %K Growth rate %K Size effect %Z MSC 2010: 60H10; 91B26; 91G10. %Z Mathematics [math]/Probability [math.PR] %Z Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM]Preprints, Working Papers, ... %X 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. %G English %2 https://enpc.hal.science/hal-00921151v2/document %2 https://enpc.hal.science/hal-00921151v2/file/mfatlas_AF.pdf %L hal-00921151 %U https://enpc.hal.science/hal-00921151