Stochastic effects in a discretized kinetic model of economic exchange

M.L. Bertotti, A.K. Chattopadhyay, G. Modanese*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker–Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.
    Original languageEnglish
    Pages (from-to)724–732
    Number of pages9
    JournalPhysica A
    Early online date26 Dec 2016
    Publication statusPublished - 1 Apr 2017

    Bibliographical note

    © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International


    • discretized Boltzmann equation
    • stochastic differential equations
    • income distributions
    • economic inequality
    • social mobility


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