On a kinetic model for a simple market economy. (English) Zbl 1133.91474

Summary: We consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis.


91B80 Applications of statistical and quantum mechanics to economics (econophysics)
91B54 Special types of economic markets (including Cournot, Bertrand)
Full Text: DOI arXiv


[8] Degond P., Pareschi L., Russo G. Modelling and Numerical Methods for Kinetic Equations (Birkhauser, 2004) · Zbl 1054.76004
[20] Pareschi L. (2004). Microscopic dynamics and mathematical modelling of a market economy: kinetic equations and numerical methods, (preprint)
[21] Pareto V. (1897). Cours d’Economie Politique, Rouge and Pichon, eds. (Lausanne and Paris)
[24] Solomon S., Stochastic Lotka-Volterra systems of competing auto-catalytic agents lead generically to truncated Pareto power wealth distribution, truncated Levy distribution of market returns, clustered volatility, booms and crashes, in Computational Finance 97, A.-P. N. Refenes, Burgess AN., and Moody JE., eds. (Kluwer Academic Publishers, Dordrecht 1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.