Long time behaviour and mean-field limit of Atlas models

Julien Reygner (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

This article reviews a few basic features of systems of one-dimensional diffusions with rank-based characteristics. Such systems arise in particular in the modelling of financial markets , where they go by the name of Atlas models. We mostly describe their long time and large scale behaviour, and lay a particular emphasis on the case of mean-field interactions. We finally present an application of the reviewed results to the modelling of capital distribution in systems with a large number of agents.

Domaines: Probabilités [math.PR]

Julien Reygner. Long time behaviour and mean-field limit of Atlas models. ESAIM: Proceedings and Surveys, 2017, Journées MAS 2016 de la SMAI – Phénomènes complexes et hétérogènes, 60, pp.132-143. ⟨10.1051/proc/201760132⟩. ⟨hal-01525360⟩