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B. Düring, D. Matthes, G. Toscani:
"Kinetic equations modelling wealth redistribution: a comparison of approaches";
in: "ASC Report 16/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-018.

Kinetic equations modelling the redistribution of wealth in simple market economies is one of the
major topics in the field of econophysics. We present a unifying approach to the qualitative study
for a large variety of such models, which is based on a moment analysis in the related homogeneous
Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence,
we are able to classify the most important feature of the steady wealth distribution, namely the
fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters.
Our results apply e.g. to the market model with risky investments [S. Cordier, L. Pareschi and G.
Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [B.K.
Chakrabarti, A. Chatterjee and S.S. Manna, Physica A 335, 155 (2004)]. Also, we present results
from numerical experiments that confirm the theoretical predictions.

http://www.asc.tuwien.ac.at/preprint/2008/asc16x2008.pdf

Project Head Ansgar Jüngel:
Entropie-Entropiedissipationsmethoden für nichtlineare partielle Differentialgleichungen höherer Ordnung (Postdoc-Stelle für Herrn Dr. Daniel Matthes)

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