Kinetic equations modelling wealth redistribution: A comparison of approaches
Kinetic equations modelling wealth redistribution: A comparison of approaches
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DOI：
10.1103/physreve.78.056103
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发表时间：
2008-11-01
影响因子：
2.4
通讯作者：
Toscani, Giuseppe
中科院分区：
文献类型：
--
作者：
Duering, Bertram;Matthes, Daniel;Toscani, Giuseppe
对简单市场经济中财富再分配进行建模的动力学方程是经济物理学领域的主要课题之一。我们提出了一种对多种此类模型进行定性研究的统一方法，该方法基于相关齐次玻尔兹曼方程中的矩分析，以及使用合适的概率度量指标。因此，我们能够根据模型参数对稳定财富分配最重要的特征（即帕累托尾部的肥厚程度）和后者的动态稳定性进行分类。我们的结果适用于例如风险投资的市场模型 [S. Cordier，L. Pareschi，G. Toscani，J. Stat。物理。 120, 253 (2005)]，以及具有抑制储蓄倾向的模型 [A. Chatterjee、B.K.Chakrabarti 和 S.S.Manna，Physica A 335, 155 (2004)]。此外，我们还提出了数值实验的结果，证实了理论预测。
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 [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.