# American Institute of Mathematical Sciences

June  2010, 3(2): 223-239. doi: 10.3934/krm.2010.3.223

## 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  October 2009 Revised  December 2009 Published  May 2010

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.
Citation: Marzia Bisi, Giampiero Spiga. A Boltzmann-type model for market economy and its continuous trading limit. Kinetic and Related Models, 2010, 3 (2) : 223-239. doi: 10.3934/krm.2010.3.223
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