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B. Düring, D. Matthes, G. Toscani:
"A Boltzmann-type approach to the formation of wealth distribution curves";
in: "ASC Report 29/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

Kinetic market models have been proposed recently to account for the
redistribution of wealth in simple market economies. These models allow
to develop a qualitative theory, which is based on methods borrowed from
the kinetic theory of rarefied gases. The aim of these notes is to present
a unifying approach to the study of the evolution of wealth in the large-
time regime. The considered models are divided into two classes: the first
class is such that the society´s mean wealth is conserved, while for models
of the second class, the mean wealth grows or decreases exponentially in
time. In both cases, it is possible to classify the most important feature
of the steady (or self-similar, respectively) wealth distributions, namely
the fatness of the Pareto tail. We shall also discuss the tails´ dynamical
stability in terms of the model parameters. Our results are derived by
means of a qualitative analysis of the associated homogeneous Boltzmann
equations. The key tools are suitable metrics for probability measures,
and a concise description of the evolution of moments. A recent extension
to economies, in which different groups of agents interact, is presented in
detail. We conclude with numerical experiments that confirm the theo-
retical predictions.

Econophysics, Boltzmann equation, wealth and income dis-

http://www.asc.tuwien.ac.at/preprint/2008/asc29x2008.pdf

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