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...

An existence theorem for a bias of the mean in the presence of data dispersion is proved. The ultimate aims are to use this theorem to explain the well-known problems of utility and decision theories, such as risk aversion, the underweighting of high and the overweighting of low probabilities,...