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2010, Volume 3, Issue 2: 223-239. Doi: 10.3934/krm.2010.3.223
This issue Previous Article On half-space problems for the weakly non-linear discrete Boltzmann equation Next Article On the plasma-charge model

A Boltzmann-type model for market economy and its continuous trading limit

  • 1.

    Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, I-43100 Parma

  • 2.

    Dipartimento di Matematica, Universitá di Parma, V.le G.P. Usberti 53/A, 43100 Parma

Received:  September 30, 2009
Revised:  November 30, 2009
Published:  May 2010
Abstract Related Papers Cited by
    Abstract
  • In the frame of a kinetic Boltzmann-type approach to modeling market economies, a random conservative-in-the-mean scheme is proposed for binary transactions among agents. The scheme extends a very successful model recently introduced by Cordier, Pareschi and Toscani. Effects of the risky market on the overall output after the trade of each agent are accounted for by random variables affecting not only the wealth of that agent before the trade, but also the one of his partner. Variations induced by this generalization on steady distribution, existence of moments, and Pareto index are discussed. In particular, the continuous trading limit and the relevant limiting Fokker-Planck equation are commented on in detail.
    Mathematics Subject Classification: 82C40, 91B60, 35B40.

    Citation:
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