A stochastic version of Zeeman's market model

Studies in Nonlinear Dynamics and Econometrics

Volumn 8, Issue 4, 2004, Pages

  Rheinlaender, Thorsten ^a   Steinkamp, Marcus ^b  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14844283753     PISSN: 15583708     EISSN: 10811826     Source Type: Journal    
DOI: 10.2202/1558-3708.1111     Document Type: Article

References (19)

1. Arnold, L. (1998): Random dynamical systems. Berlin-Heidelberg-New York: Springer.
2. Arnold, L., and P. Boxler (1992): "Stochastic bifurcation: instructive examples in dimension one," in M. Pinsky and V. Wihstutz, eds., Diffusion processes and related problems in analysis, volumeII: Stochastic flows, Progress in Probability, 27, Boston-Basel-Stuttgart: Birkhäuser, 241-255.
3. Arnold, L., and P. Imkeller (1998): "Normal forms for stochastic differential equations," Probability Theory and Related Fields, 110, 559-588.
4. Chiarella, C., R. Died and L. Gardini (2001): "Asset price dynamics in a financial market with fundamentalists and chartists," Discrete Dynamics in Nature and Society, 6, 69-99.
5. Crauel, H., and F. Flandoli (1998): "Additive noise destroys a pitchfork bifurcation," Journal of Dynamics and Differential Equations, 10, 259-274.
6. Crauel, H., P. Imkeller and M. Steinkamp (1999): "Bifurcation of one-dimensional stochastic differential equations," in H. Crauel and M. Gundlach, eds., Stochastic dynamics. New York: Springer, 27-47.
7. Föllmer, H., and M. Schweizer (1993): " A microeconomic approach to diffusion models for stock prices," Mathematical Finance, 3, 1-23.
8. Gaunersdorfer, A., and C. H. Hommes (2000): "A nonlinear structural model for volatility clustering," University of Vienna: SFB-WP No. 63 (Adaptive information systems and modelling in economics and management science).
9. Gihman, I. I., and A. V. Skorohod (1972): Stochastic different eguations. Berlin-Heidelberg-New York: Springer.
10. Golubitsky, M., and D. G. Schaeffer (1985): Singularities and groups in bifurcation. Berlin-Heidelberg-New York: Springer.
11. Jetschke, G. (1989): Mathematik der Selbstorganization. Berlin: VEB.
12. Kurtz, T. G., and P. Protter (1991): "Weak limit theorems for stochastic integrals and stochastic differential equations," Annals of Probability, 19, 1035-1070.
13. Kuznetsov, Y. A. (1995): Elements of applied bifurcation theory. Berlin-Heidelberg-New York: Springer.
14. Ledrappier, F., and L. S. Young (1988): "Entropy for random transformations," Probability Theory and Related Fields, 80, 217-240.
15. Lux, T., and M. Marchesi (2000): "Volatility clustering in financial markets: a micro-simulation of interacting agents," International Journal of Theoretical and Applied Finance, 3, 675-702.
16. Steinkamp, M. (2000): Bifurcations of one dimentional stochastic differential equation. Phd-thesis, Humboldt University of Berlin, and Berlin: Logos Verlag (2001).
17. Thurner, S., E.J. Dockner and A. Gaunersdorfer (2002): " Asset price dynamics in a model of investors operating on different time horizons, " University of Vienna: Preprint.
18. Zeeman, E. C. (1974): "On the unstable behavior of stock exchanges," Journal of Mathematical Economics, 1, 39-49.
19. Zeeman, E. C. (1988): "Stability of dynamical systems," Nonlinearity, 1, 115-155.