On a kinetic model for a simple market economy

Journal of Statistical Physics

Volumn 120, Issue 1-2, 2005, Pages 253-277

  Cordier, Stephane ^a   Pareschi, Lorenzo ^b   Toscani, Giuseppe ^c  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b UNIVERSITY OF FERRARA   (Italy)

^c UNIVERSITY OF PAVIA   (Italy)

Author keywords

Boltzmann equation; Econophysics; Pareto distribution; Wealth and income distributions

Indexed keywords

EID: 24644516564     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-5456-0     Document Type: Article

References (25)

1. A. Baldassarri, U. Marini Bettolo Marconi, and A. Puglisi, Kinetic models of inelastic gases, Math. Mod. Methods. Appl. Sci. 12:965-983 (2002).
2. A. V Bobylev, The theory of the spatially uniform Boltzmann equation for Maxwell molecules, Sov Sci Rev C 7:112-229 (1988).
3. A. V Bobylev, J. A- Carrillo, and I. Gamba, On some properties of kinetic and hydrodynamics equations for inelastic interactions, J. Statist. Phys. 98:743-773 (2000).
4. J. P. Bouchaud, and M. Mézard, Wealth condensation in a simple model of economy, Physica A 282:536-545 (2000).
5. C. Cercignani, R. Illner, and M. Pulvirenti, The mathematical theory of dilute gases, Springer Series in Applied Mathematical Sciences, Vol. 106 (Springer-Verlag, Berlin 1994.)
6. A.Chakraborti, Distributions of money in models of market economy, Int. J. Modern Phys. C 13:1315-1321(2002).
7. A. Chakraborti, and B. K. Chakrabarti, Statistical mechanics of money: how saving propensity affects its distributions, Eur. Phys. J. B. 17:167-170 (2000).
8. P. Degond, L. Pareschi, and G. Russo, Modelling and Numerical Methods for Kinetic Equations (Birkhauser, 2004).
9. M. H. Ernst, and R. Brito, High energy tails for inelastic Maxwell models. Europhys. Lett. 43:497-502 (2002).
10. M.H. Ernst, and R. Brito, Scaling solutions of inelastic Boltzmann equation with over-populated high energy tails. J. Statist. Phys. 109:407-432 (2002).
11. A. Drǎgulescu, and V. M. Yakovenko, Statistical mechanics of money, Eur. Phys. J. B 17:723-729 (2000).
12. X. Gabaix, P. Gopikrishnan, V. Plerou, and H. E. Stanley, A theory of power-law distributions in financial market fluctuations, Nature 423:267-270 (2003).
13. B. Hayes, Follow the money, Am. Scientist 90,(5):400-405 (2002).
14. S. Ispolatov, P. L. Krapivsky, and S. Redner, Wealth distributions in asset exchange models, Eur. Phys. J. B 2:267-276 (1998).
15. A. Klar, and R. Wegener, A kinetic model for vehicular traffic derived from a stochastic microscopic model, Transp. Theory Stat. Phys. 25(7):78 5-798 (1996).
16. H. Levy, M. Levy, and S. Solomon, Microscopic simulations of financial markets (Academic Press, New York, 2000).
17. O. Malcai, O. Biham, S. Solomon, and P. Richmond, Theoretical analysis and simulations of the generalized Lotka-Volterra model, Phys. Rev. E 66:031102 (2002).
18. B.Mandelbrot, The Pareto-Lévy law and the distribution of income, Int. Economic Rev. 1:79-106 (1960).
19. S. McNamara, and W. R. Young, Kinetics of a one-dimensional granular medium in the quasi-elastic limit, Phys. Fluids A 5:34-45 (1993).
20. L. Pareschi, Microscopic dynamics and mathematical modelling of a market economy: kinetic equations and numerical methods, (preprint) (2004).
21. V. Pareto, Cours d'Economie Politique, Rouge and Pichon, eds. (Lausanne and Paris, 1897).
22. V. Plerou, P. Gopikrishnan, and H. E. Stanley, Econophysics: two-phase behaviour of financial markets, Nature 421:130 (2003) (cond-mat/0111349).
23. F. Slanina, Inelastically scattering particles and wealth distribution in an open economy, Phys. Rev. E 69:046102 (2004). (cond-mat/0311025).
24. S. Solomon, Stochastic Lotka-Volterra systems of competing auto-catalytic agents lead generically to truncated Pareto power wealth distribution, truncated Levy distribution of market returns, clustered volatility, booms and crashes, in Computational Finance 97, A.-P. N. Refenes, A. N. Burgess, and J. E. Moody, eds. (Kluwer Academic Publishers, Dordrecht 1998).
25. G. Toscani, One-dimensional kinetic models of granular flows, RAIRO Modél Math. Anal. Numér. 34:1277-1292 (2000).