Heterogeneous Speculators and Asset Price Dynamics: Further Results from a One-Dimensional Discontinuous Piecewise-Linear Map

Computational Economics

Volumn 38, Issue 3, 2011, Pages 329-347

  Tramontana, Fabio ^a   Gardini, Laura ^b   Westerhoff, Frank ^c  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSITY OF URBINO   (Italy)

^c UNIVERSITY OF BAMBERG   (Germany)

Author keywords

Adding scheme; Border collision bifurcation; Bull and bear dynamics; Discontinuous piecewise smooth map; Financial crises

Indexed keywords

EID: 80052921551     PISSN: 09277099     EISSN: 15729974     Source Type: Journal    
DOI: 10.1007/s10614-011-9284-9     Document Type: Article

References (39)

1. Avrutin V., Schanz M. (2006) Multi-parametric bifurcations in a scalar piecewise-linear map. Nonlinearity 19: 531-552.
2. Avrutin V., Schanz M., Banerjee S. (2006) Multi-parametric bifurcations in a piecewise-linear discontinuous map. Nonlinearity 19: 1875-1906.
3. Avrutin V., Schanz M., Gardini L. (2010) Calculation of bifurcation curves by map replacement. International Journal of Bifurcation and Chaos 20(10): 3105-3135.
4. Banerjee S., Karthik M. S., Yuan G., Yorke J. A. (2000) Bifurcations in one-dimensional piecewise smooth maps-theory and applications in switching circuits. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47: 389-394.
5. Banerjee S., Yorke J. A., Grebogi C. (1998) Robust chaos. Physical Review Letters 80: 3049-3052.
6. Boswijk P., Hommes C., Manzan S. (2007) Behavioral heterogeneity in stock prices. Journal of Economic Dynamics and Control 31: 1938-1970.
7. Brock W., Hommes C. (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control 22: 1235-1274.
8. Chiarella C. (1992) The dynamics of speculative behavior. Annals of Operations Research 37: 101-123.
9. Chiarella C., Dieci R., Gardini L. (2002) Speculative behaviour and complex asset price dynamics: A global analysis. Journal of Economic Behavior and Organization 49: 173-197.
10. Chiarella C., Dieci R., He X.-Z. (2009) Heterogeneity, market mechanisms, and asset price dynamics. In: Hens T., Schenk-Hoppé K. R. (eds) Handbook of Financial Markets: Dynamics and Evolution. North-Holland, Amsterdam, pp 277-344.
11. Day R. (1997) Complex dynamics, market mediation and stock price behavior. North American Actuarial Journal 1: 6-23.
12. Day R., Huang W. (1990) Bulls, bears and market sheep. Journal of Economic Behavior and Organization 14: 299-329.
13. De Grauwe P., Dewachter H., Embrechts M. (1993) Exchange rate theory-chaotic models of foreign exchange markets. Blackwell, Oxford.
14. Franke R. (2009) A prototype model of speculative dynamics with position-based trading. Journal of Economic Dynamics and Control 33: 1134-1158.
15. Gardini L., Tramontana F., Avrutin V., Schanz M. (2010) Border collision bifurcations in 1D PWL map and the Leonov approach. International Journal of Bifurcation and Chaos 20(10): 3085-3104.
16. Hao B.-L. (1989) Elementary symbolic dynamics and chaos in dissipative systems. World Scientific, Singapore.
17. Hommes C. H., Sonnemans J., Tuinstra J., van de Velden H. (2005) Coordination of expectations in asset pricing experiments. Review of Financial Studies 18: 955-980.
18. Hommes C. H., Wagener F. (2009) Complex evolutionary systems in behavioral finance. In: Hens T., Schenk-Hoppé K. R. (eds) Handbook of financial markets: Dynamics and evolution. North-Holland, Amsterdam, pp 217-276.
19. Huang W., Day R. (1993) Chaotically switching bear and bull markets: the derivation of stock price distributions from behavioral rules. In: Day R., Chen P. (eds) Nonlinear dynamics and evolutionary economics. Oxford University Press, Oxford, pp 1-49.
20. Huang W., Zheng H., Chia W.-M. (2010) Financial crises and interacting heterogeneous agents. Journal of Economic Dynamics and Control 34: 1105-1122.
21. Leonov N. N. (1959) Map of the line onto itself. Radiofisica 3: 942-956.
22. Leonov N. N. (1962) Discontinuous map of the straight line. Dohk Ahad Nauk SSSR 143: 1038-1041.
23. Lux T. (1995) Herd behavior, bubbles and crashes. Economic Journal 105: 881-896.
24. Lux, T. (2006). Financial power laws: Empirical evidence, models and mechanisms. Economics Working Paper No 2006-12, University of Kiel.
25. Lux T. (2009) Stochastic behavioural asset-pricing models and the stylize facts. In: Hens T., Schenk-Hoppé K. R. (eds) Handbook of Financial Markets: Dynamics and Evolution. North-Holland, Amsterdam, pp 161-216.
26. Maistrenko Y. L., Maistrenko V. L., Chua L. O. (1993) Cycles of chaotic intervals in a time-delayed Chua's circuit. International Journal of Bifurcation and Chaos 3: 1557-1572.
27. Maistrenko Y. L., Maistrenko V. L., Vikul S. I. (1998) On period-adding sequences of attracting cycles in piecewise linear maps. Chaos, Solitons & Fractals 9: 67-75.
28. Maistrenko Y. L., Maistrenko V. L., Vikul S. I., Chua L. O. (1995) Bifurcations of attracting cycles from time-delayed Chua's circuit. International Journal of Bifurcation and Chaos 5: 653-671.
29. Menkhoff L., Taylor M. (2007) The obstinate passion of foreign exchange professionals: technical analysis. Journal of Economic Literature 45: 936-972.
30. Mira C. (1978) Sur les structure des bifurcations des diffeomorphisme du cercle. Comptes Rendus de l'Academie des Sciences Paris, Series A 287: 883-886.
31. Mira C. (1987) Chaotic dynamics. World Scientific, Singapore.
32. Nusse H. E., Ott E., Yorke J. A. (1994) Border-collision bifurcations: An explanation for observed bifurcation phenomena. Physical Review E 49: 1073-1076.
33. Nusse H. E., Yorke J. A. (1992) Border-collision bifurcations including period two to period three for piecewise smooth systems. Physica D 57: 39-57.
34. Sushko I., Gardini L. (2010) Degenerate bifurcations and border collisions in piecewise smooth 1D and 2D maps. International Journal of Bifurcation & Chaos 20(7): 2045-2070.
35. Tramontana F., Gardini L., Westerhoff F. (2010a) Intricate asset price dynamics and one-dimensional discontinuous maps. In: Puu T., Panchuck A. (eds) Nonlinear Economic Dynamics. Nova Science Publishers, New York.
36. Tramontana F., Westerhoff F., Gardini L. (2010b) On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders. Journal of Economic Behavior and Organization 74: 187-205.
37. Westerhoff F. (2009) Exchange rate dynamics: A nonlinear survey. In: Rosser J. B. (eds) Handbook of research on complexity. Edward Elgar, Cheltenham, pp 287-325.
38. Westerhoff F., Dieci R. (2006) The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: a behavioral finance approach. Journal of Economic Dynamics and Control 30: 293-322.
39. Westerhoff, F. & Franke, R. (2010, in press). Converse trading strategies, intrinsic noise and the stylized facts of financial markets. Quantitative Finance.