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Hydrodynamics from kinetic models of conservative economies

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  • Düring, B.
  • Toscani, G.

Abstract

In this paper, we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge of the homogeneous steady wealth distribution (the Maxwellian) of the underlying kinetic model. The collision operator used here is the Fokker–Planck operator introduced by J.P. Bouchaud and M. Mezard [Wealth condensation in a simple model of economy, Physica A 282 (2000) 536–545], which has been recently obtained in a suitable asymptotic of a Boltzmann-like model involving both exchanges between agents and speculative trading by S. Cordier, L. Pareschi and one of the authors [S. Cordier, L. Pareschi, G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys. 120 (2005) 253–277]. Numerical simulations on the fluid equations are then proposed and analyzed for various laws of variation of the propensity.

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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 384 (2007)
Issue (Month): 2 ()
Pages: 493-506

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Handle: RePEc:eee:phsmap:v:384:y:2007:i:2:p:493-506

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Wealth and income distributions; Boltzmann equation; Hydrodynamics; Euler equations;

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  1. Romanovsky, M. & Oks, E., 2001. "Time intervals distribution of stock transactions and time correlation of stock indices in the model space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 168-174.
  2. Chatterjee, Arnab & K. Chakrabarti, Bikas & Manna, S.S, 2004. "Pareto law in a kinetic model of market with random saving propensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 155-163.
  3. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
  4. Yougui Wang & Ning Ding & Li Zhang, 2005. "The Circulation of Money and Holding Time Distribution," Papers physics/0507147, arXiv.org.
  5. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA.
  6. Arnab Chatterjee & Bikas K. Chakrabarti & S. S. Manna, 2003. "Pareto Law in a Kinetic Model of Market with Random Saving Propensity," Papers cond-mat/0301289, arXiv.org, revised Jan 2004.
  7. Wang, Yougui & Ding, Ning & Zhang, Li, 2003. "The circulation of money and holding time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 665-677.
  8. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
  9. F. Slanina & H. Lavicka, 2003. "Analytical results for the Sznajd model of opinion formation," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 35(2), pages 279-288, September.
  10. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
  11. Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Master equation for a kinetic model of trading market and its analytic solution," Papers cond-mat/0501413, arXiv.org, revised Aug 2005.
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Cited by:
  1. 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.
  2. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics: agent-based models," Post-Print hal-00621059, HAL.
  3. G. Toscani & C. Brugna & S. Demichelis, 2012. "Kinetic models for the trading of goods," Papers 1208.6305, arXiv.org.

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