The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

SPATIALLY HOMOGENEOUS GLOBAL PRICE DYNAMICS ON A CHAIN OF LOCAL MARKETS

  • Published : 2009.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

The main purpose of this paper is to use the methods of Lattice Dynamical System to establish a global model, which extends the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution over an infinite chain of many local markets interacting each other through a diffusion of prices between them. For brevity of the model, we assume linear decreasing demands and quadratic supplies with naive predictors, and investigate the spatially homogeneous global price dynamics and show that the dynamics is topologically conjugate to that of well-known logistic map and hence undergoes a period-doubling bifurcation route to chaos as a parameter varies through a critical value.

Keywords

References

  1. Afraimovich, V. S. & Bunimovich, L. A.: Simplest structures in coupled map lattices and their stability. preprint in GIT (1992).
  2. Barucci, E.: Exponentially fading memory learning in a forward looking economic models. Journal of Economic Dynamics and Control 24 (2000), no. 5-7, 1027-1046. https://doi.org/10.1016/S0165-1889(99)00035-4
  3. Beckmann, M. J. & Puu, T.: Spatial economics: Density, Potential, and Flow. North­-Holland, Amsterdam, 1985.
  4. Benhabib, J. & Day, R. H.: A Characterization of erratic dynamics in the Overlapping Generations Model. Journal of Economic Dynamics & Control 4 (1982), 37-55. https://doi.org/10.1016/0165-1889(82)90002-1
  5. Bohm, V. & Chiarella, C.: Mean Variance Preferrences, Expectations Formation, and the Dynamics of Random Asset Prices. Mathematical Finance 15 (2005), no. 1, 61-97. https://doi.org/10.1111/j.0960-1627.2005.00211.x
  6. Brock, W. A. & Hommes, C. H. : 1A Rational Route to Randomness. Econometrica 65 (1997), no. 5, 1059-1095. https://doi.org/10.2307/2171879
  7. Brock, W. A. & Hommes, C. H. : Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model. Journal of Economic Dynamics and Control 22 (1998), 1235-1274. https://doi.org/10.1016/S0165-1889(98)00011-6
  8. Brock, W. A., Hommes, C. H. & Wagner, F.O.O.: Evolutionary dynamics in markets with many trader types. Journal of Mathematical Economics 41 (2005), 7-42. https://doi.org/10.1016/j.jmateco.2004.02.002
  9. Bunimovich, L. A. et al: Trivial Maps. Chaos 2 (1992).
  10. Bunimovich, L. A. & Sinai, Y. G.: 1988. Spacetime Chaos in Coupled Map Lattices. Nonlinearity 1 (1998), 491-516. https://doi.org/10.1088/0951-7715/1/4/001
  11. Chiarella, C., Dieci, R. & He, X.: Heterogeneous Expectations and Speculative Behavior in a Dynamic Multi-Asset Framework. Research paper 166. Quantitative Finance Research Center. University of Technology Sydney, 2005.
  12. Chiarella, C., He, X. & Hommes, C.: A dynamic analysis of moving average rules. Journal of Economic Dynamics & Control 30 (2006), 1729-1753. https://doi.org/10.1016/j.jedc.2005.08.014
  13. Chiarella, C., Dieci, R. & Gardini, L.: Asset price and wealth dynamics in a financial market with heterogeneous agents. Journal of Economic Dynamics & Control 30 (2006), 1755-1786. https://doi.org/10.1016/j.jedc.2005.10.011
  14. Choudhary, M. A. & Orszag, J. M.: A cobweb model with local externalities. Journal of Economic Dynamics & Control (2007).
  15. Devaney, R. L.: An introduction to Chaotic Dynamical Systems. Addison-Wesley, 1989.
  16. Goeree, J. K. & Hommes, C. H.: Heterogeneous beliefs and the non-linear cobweb model. Journal of Economic Dynamics & Control 24 (2000), 761-798. https://doi.org/10.1016/S0165-1889(99)00025-1
  17. Hommes, C. H.: On the consistency of backward-looking expectations: The case of the cobweb. Journal of Economic Behavior & Organization 33 (1998), 333-362. https://doi.org/10.1016/S0167-2681(97)00062-0
  18. Hommes, C., Huang, H. & Wang, D.: 2005. A robust rational route to randomness in a simple asset pricing model. Journal of Economic Dynamics & Control 29 (2005), 1043-1072. https://doi.org/10.1016/j.jedc.2004.08.003
  19. Kaneko, K.: Theory and applitions of coupled map lattices. John-Wiley and Sons, 1993.
  20. Niss, M.: History of the Lenz-Ising Model 1920-1950: From Ferromagnetic to Cooperative Phenomena. Archive for History of Exact Scineces 59 (2005), 267-318. https://doi.org/10.1007/s00407-004-0088-3
  21. Robinson, C.: Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. CRC Press