Düring, B., & Matthes, D. (2010). A mathematical theory for wealth distribution. In G. Naldi, L. Pareschi, & G. Toscani (Eds.), Modeling and Simulation in Science, Engineering and Technology. Birkhäuser. https://doi.org/10.1007/978-0-8176-4946-3_4
Boltzmann equation; econophysics; Wealth distribution
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Abstract:
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.
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Project title:
Numerics and modeling of nonlinear partial differential equations for the description of credit and price risks (Deutsche Forschungsgemeinschaft) Kinetic wealth distribution models and diffusive limit equations (OeAD Österr.Austauschdienst GmbH Geschäftsstelle Wien)
