Could Markets' Equilibrium Sets Be Fractal Attractors?

Dominique, C-Rene (2009): Could Markets' Equilibrium Sets Be Fractal Attractors?

Abstract

The assumption that markets are positive linear structures moving toward stable fixed-point equilibria is not supproted by empirical investigations.This note reformulates the purest and the simplestof all Walrasian models, i. e.,a pure exchange economy, and shows that even such a simple market moves toward a compact time-invariant set of prices due to the constant destruction and creation of excess demands under the impulsion of self-interested agents with strong monotone preferences. Fractal attractors better explain continuous market fluctuations, 'black swans', and the flawed risk assessments of market risks of the financial engineers of Wall Street.

• Item Type: MPRA Paper
• Language: English
• Keywords: Market Equilibria, Market Fluctuations, Black Swans, Risk Assessment
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D50 - General

References

REFERENCES

Arrow, K., J. and Debreu, G. (1954). “Existence of an Equilibrium for a Competitive Economy.” Econometrica, 22, 265-90.

-----------------, Brock, D. H. and Hurwicz, L (1958). “On the Stability of Competitive Equilibrium I.” Econometrica, 27, 82-109. ---------------and Hurwicz, L. (1959). “On the Stability of Competitive Equilibrium II.” Econometrica, 26, 522-52.

Brock, W. (1986). “Distinguishing Random and Deterministic Systems: Abridged Version. Journal of Econ. Theory, 40, 168-95.

Cantor, G. (1883).”Grundlagen einer allegemein manichfaltigheitslehre.” Math. Annalen, 21, 545-91.

Casti, J. L. (1994). Complexification. New York: Harper Perennial.

Dominique, C-R. (2008a). “Walrasian Solutions Without Utility Functions. MPRA Paper no. 8759. University Library of Munich; see also Economics and Econometrics Institute Research Papers Series no. 10/2008.

-----------------(2008b). “Behind the 2008 Capital Market Collapse.” The Economic and Econometrics Insti- tute Research Papers Series no. 17/2008.

Frobenius, G. (1908). “ Uber Matrizen aus positiven Elementen.” Sitzungsberichte Konizl Preussichen Akad. Wiss.” 8, 471-76.

Frank, M., Gencay, R, and Stengos, T. (1988a) “International Chaos.” European Economic Jour., 32, 1569-84.

Grassberger, P. and Procaccia, I. (1983). “Measuring the Strangeness of Strange Attractors.” Physica, 9D, 189-208.

Hausdorff, F. (1919). Dimension und ausseres.” Mathematische Annalen, 79, 157-79.

Hurst, H. et al. (1951). Long Term Storage: An Experimental Study. London: Constable.

Koch, H. von (1904). “Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire.” Arkiv for Matematik Astronomi och Fysik, 1, 681-704. Mandelbrot, B. (1983a). The Fractal Geometry of Nature. New York: W. H. Freeman.

--------------- (1983b). “On Fractal Geometry and a Few of the Mathematical Questions It Has Raised.” Proceedings of the International Congress of Mathematicians. Warsaw: August, 1661-75.

Marotto, F. R. (1979). “Snap-Back Repeller Implies Chaos in Rn ”, Jour. of Math. Analysis and Applications, 72, 199-223

Metzler, L. A. (1945). “Stability of Multiple Markets: The Hicks Conditions.” Econometrica, 13, 277-92.

Mitchell, W. C. and Thorpe, W. L. (1926). Business Annals, New York: Nat. Bur. of Econ. Research.

Peters, E. (1989). Fractal Structure in the Capital Market.” Financial Analyst Jour., July/August.

-------------(1991). “A Chaotic Attractor for the S&P-500.” Financial Analyst Jour., March/April.

Perron, O. (1907). Zur Theorie der Matrizen.” Math. Annalen, 64, 432-45.

Walras, L (1883). Théorie mathématique de la richesse Sociale. Corbaz: Lausanne.

------------(1900). Eléments d’économie politique ou théorie de la production de la richesse sociale, 4th ed. Paris: Pichon.

Copyright Ó 2008 by C-René Dominique. *