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B. Düring, D. Matthes:
"A mathematical theory for wealth distribution";
in: "Mathematical modeling of collective behavior in socio-economic and life-sciences", G. Naldi, L. Pareschi, G. Toscani (ed.); Birkhäuser, Boston, 2010, (invited), ISBN: 978-0-8176-4945-6, 81 - 113.

We review a qualitative mathematical theory of kinetic models for wealth distribution in simple market economies. This theory is a unified approach that covers a wide class of such models which have been proposed in the recent literature on econophysics. Based on the analysis of the underlying homogeneous Boltzmann equation, a qualitative description of the evolution of wealth in the large-time regime is obtained. In particular, the most important features of the steady wealth distribution are classified, namely the fatness of the Pareto tail and the tails' dynamical stability. Most of the applied methods are borrowed from the kinetic theory of rarefied gases. A concise description of the moment hierarchy and suitable metrics for probability measures are employed as key tools.

s. engl. Abstract

Wealth distribution, Boltzmann equation, econophysics

http://dx.doi.org/10.1007/978-0-8176-4946-3

Project Head Bertram Düring:
Kinetische Vermögensverteilungsmodelle und diffusive Grenzwert-Gleichungen

Project Head Ansgar Jüngel:
Numerik und Modellierung nichtlinearer partieller Differentialgleichungen zur Beschreibung von Kredit- und Preisrisiken