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

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Author Info
Arnab Chatterjee
Bikas K. Chakrabarti
Robin B. Stinchcombe
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 $\nu$ 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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File URL: http://arxiv.org/abs/cond-mat/0501413
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number cond-mat/0501413.

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Date of creation: Jan 2005
Date of revision: Aug 2005
Publication status: Published in Phys. Rev. E 72 (2005) 026126
Handle: RePEc:arx:papers:cond-mat/0501413

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  1. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical Mechanics of Money, Wealth, and Income," Quantitative Finance Papers 0905.1518, arXiv.org. [Downloadable!]
  2. B. Düring & G. Toscani, 2007. "Hydrodynamics from kinetic models of conservative economies," CoFE Discussion Paper 07-06, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  3. Bertram Düring & Giuseppe Toscani, 2008. "International and Domestic Trading and Wealth Distribution," CoFE Discussion Paper 08-02, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
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