Abstract
We give a microscopic representation of the stock-market in which the microscopic agents are the individual traders and their capital. Their basic dynamics consists in the auto-catalysis of the individual capital and in the global competition/cooperation between the agents mediated by the total wealth/index of the market. We show that such systems lead generically to (truncated) Pareto power-law distribution of the individual wealth. This, in turn, leads to intermittent market returns parametrized by a (truncated) Levy-stable distribution. We relate the truncation in the Levy-stable distribution to the fact that at each moment no trader can own more than the total wealth in the market. In the cases where the system is dominated by the largest traders, the dynamics looks similar to noisy low-dimensional chaos. By introducing traders memory and/or feedback between global and individual wealth fluctuations, one obtains auto-correlations in the time evolution of the “volatility” as well as market booms and crashes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Solomon, in Annual Reviews of Computational Physics I, Ed. D. Stauffer, p. 243 (World Scientific, 1995) ai.]2)_Pareto V. Cours d’Economique Politique, Vol 2, (1897). Manual of Political Economy, Macmilan G.K. Zipf, Human Behaviour and the Principle of Least Effort Addison Wesley Press, Cambridge MA (1949).
P. Levy, Theorie de l’Addition des Variables Aleatoires Gauthier-Villiers, Paris, 1937. E.W. Montroll and M.F. Shlesinger, Proc. Nat. Acad. Sci. USA 79 (1982) 3380. R.N. Mantegna and H.E. Stanley in Levy Flights and Related Topics in Physics, Eds. M.E. Shlesinger, G. Zaslavsky and U. Frisch, Springer 1995.
Mandelbrot B. B. J. Business 36, 394–419 (1963); The Fractal Geometry of Nature, Freeman, San Francisco, (1982), Econometrica 29 (1961) 517.
P.W. Anderson, J. Arrow and D. Pines, eds. The Economy as an Evolving Complex System, Redwood City, Calif.: Addison-Wesley, 1988
J. Lotka, Elements of Physical Biology, Williams and Wilkins, Baltimore 1925. V. Volterra, Nature 118 (1926) 558; R.M. May, Nature 261 (1976) 207.
S. Solomon and M. Levy International Journal of Modern Physics C, Vol. 7, No.5 (1996) 745; O. Biham, M. Levy, O. Malcai and S. Solomon preprint.
M. Levy, H. Levy and S. Solomon, Econ. Let. 45(1994)103; J. Phys 5 (1995) 1087.
H. Simon, Biometrika, vol42, Dec. 1955; Y. Ijiri and H. Simon, Skew Distributions and the Sizes of Business Firms, (North Holland, Amsterdam, 1977).
Gell-Mann M., The Quark and the Jaguar, Little Brown and Co., London 1994.
M. Levy and S. Solomon Int. J. Mod. Phys. C., Vol 7 (1996) 595
R. N. Mantegna and H. E. Stanley, Nature 383 (1996) 587; 376 (1995) 46.
Potters M., Cont R. and Bouchaud J.P. Europhys. Lett 41 (1998) 3
Bak P; Paczuski M; Shubik M. Physica A 3-4 (1997) 430.
D. Sornette and R. Cont J. Phys. I. France 7, (1997) 431; Kesten, Acta. Math. 131 (1973) 207.
M. Marsili, S. Maslov and Y-C Zhang, cond-mat/ 9801239, Caldarelli G; Marsili M; Zhang YC., Europhysics Letters 40 (1997) 479, Challet D; Zhang YC., Physica A 246 (1997) 407
M. Levy and S. Solomon Physica A 242 (1997) 90.
Takayasu Marsili et al., Phys. Rev. Lett. 79, 966 (1997)
M. Levy and S. Solomon, Int. J. Mod. Phys. C, Vol. 7, No.1 (1996) 65–72.
M. Levy, N. Persky and S. Solomon Int. J. of High Speed Computing 8 (1996)93
T. Hellthaler, Int. J. Mod. Phys. C 6 (1995) 845; D. Kohl to appear in Int. J. Mod. Phys. C.
S. Moss De Oliveira, P.M.C de Oliveira, D. Stauffer, Sex, Money, War and Computers: Nontraditional Applications of Computational Statistical Mechanics, in press 1998
Baillie R. and Bollerslev T. Review of Economic Studies 58 (1990) 565; Engle R.F., Ito T. and Lin W.-L. Econometrica 58 (1990) 525
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Solomon, S. (1998). Stochastic Lotka-Volterra Systems of Competing Auto-Catalytic Agents Lead Generically to Truncated Pareto Power Wealth Distribution, Truncated Levy-Stable Intermittent Market Returns, Clustered Volatility, Booms and Crashes. In: Refenes, AP.N., Burgess, A.N., Moody, J.E. (eds) Decision Technologies for Computational Finance. Advances in Computational Management Science, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5625-1_6
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5625-1_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-8309-3
Online ISBN: 978-1-4615-5625-1
eBook Packages: Springer Book Archive