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Hydrodynamics from kinetic models of conservative economies

  • B. Düring


    (Technische Universität Wien)

  • G. Toscani


    (Universita degli studi di Pavia)

In this paper, we introduce and discuss the passage to hy- drodynamic 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 in [4], which has been recently obtained in a suitable asymp- totic of a Boltzmann-like model involving both exchanges between agents and speculative trading by S. Cordier, L. Pareschi and one of the authors [11]. Numerical simulations on the fluid equations are then proposed and analyzed for various laws of variation of the propensity.

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Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 07-06.

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Length: 19 pages
Date of creation: 14 Jul 2007
Date of revision:
Handle: RePEc:knz:cofedp:0706
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  1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
  2. 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,, revised Aug 2005.
  3. 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,, revised Jan 2004.
  4. 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.
  5. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454,, revised Nov 2000.
  6. Yougui Wang & Ning Ding & Li Zhang, 2005. "The Circulation of Money and Holding Time Distribution," Papers physics/0507147,
  7. 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.
  8. S. Ispolatov & P.L. Krapivsky & S. Redner, 1998. "Wealth distributions in asset exchange models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 2(2), pages 267-276, March.
  9. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432,, revised Aug 2000.
  10. 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.
  11. 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.
  12. anonymous, 1980. "What’s wrong with macroeconomics," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Sum.
  13. 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.
  14. Katarzyna Sznajd-Weron & Jozef Sznajd, 2000. "Opinion evolution in closed community," HSC Research Reports HSC/00/04, Hugo Steinhaus Center, Wroclaw University of Technology.
  15. 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.
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