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Master equation for a kinetic model of trading market and its analytic solution

Arnab Chatterjee·Bikas K. Chakrabarti·Robin B. Stinchcombe
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Abstract

We analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $ν$ exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of $P(m)$. Precise solutions are then obtained in some special cases.

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Arnab Chatterjee, Bikas K. Chakrabarti, Robin B. Stinchcombe. 2005-08-22. Master equation for a kinetic model of trading market and its analytic solution. https://doi.org/10.1103/physreve.72.026126

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