A mathematical theory for wealth distribution

Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


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.


Boltzmann Equation Wealth Distribution Trade Rule Total Wealth Homogeneous Boltzmann Equation 


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Bertram Düring is supported by the Deutsche Forschungsgemeinschaft, grant JU 359/6 (Forschergruppe 518). Daniel Matthes is supported by the Deutsche Forschungsgemeinschaft, grant JU 359/7.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institut für Analysis und Scientific ComputingTechnische Universität WienWienAustria

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