The stochastic bifurcation behaviour of speculative financial markets

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 15, 2008, Pages 3837-3846

  Chiarella, Carl ^a   He, Xue Zhong ^a   Wang, Duo ^b   Zheng, Min ^a,b  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

^b PEKING UNIVERSITY   (China)

Author keywords

Heterogeneous agents; Invariant measures; Random dynamical systems; Speculative behaviour; Stochastic bifurcations

Indexed keywords

ASSET MANAGEMENT; BIFURCATION (MATHEMATICS); DYNAMICAL SYSTEMS; RANDOM PROCESSES; STOCHASTIC MODELS;

BIMODAL LOGARITHM PRICE DISTRIBUTION; HETEROGENEOUS AGENTS; INVARIANT MEASURES; RANDOM DYNAMICAL SYSTEMS; SPECULATIVE BEHAVIOR; STOCHASTIC BIFURCATIONS;

FINANCIAL DATA PROCESSING;

EID: 42649086027     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2008.01.078     Document Type: Article

References (15)

1. Arnold L. Random Dynamical Systems (1998), Springer, New York
2. Arnold L., Sri Namachchivaya N., and Schenk-Hoppé K.R. Towards an understanding of stochastic Hopf bifurcation: A case study. Int. J. Bifurcat. Chaos 6 (1996) 1947-1975
3. Beja A., and Goldman M.B. On the dynamic behaviour of prices in disequilibrium. J. Finance 35 (1980) 235-248
4. Böhm V., and Chiarella C. Mean variance preferences, expectations formation, and the dynamics of random asset prices. Math. Finance 15 (2005) 61-97
5. Chiarella C. The dynamics of speculative behaviour. Ann. Oper. Res. 37 (1992) 101-123
6. C. Chiarella, X. He, M. Zheng, The stochastic price dynamics of speculative behaviour, Working Paper, QFRC, University of Technology, Sydney, 2007
7. Crauel H., and Flandoli F. Attractors for random dynamical systems. Probab. Theory Related Fields 100 (1994) 365-393
8. H. Crauel, Invariant measures are supported by random attractors, 1995, preprint
9. Föllmer H., Horst U., and Kirman A. Equilibria in financial markets with heterogeneous agents: A probabilistic perspective. J. Math. Econom. 41 (2005) 123-155
10. Oseledets V.I. A multiplicative Ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 (1968) 197-231
11. Parker T.S., and Chua L.O. Practical Numerical Algorithms for Chaotic Systems (1989), Springer-Verlag, New York
12. Rheinlaender T., and Steinkamp M. A stochastic version of Zeeman's market model. Stud. Nonlinear Dynam. Econometrics 8 (2004) 1-23
13. Schenk-Hoppé K.R. Deterministic and stochastic Duffing-van der Pol oscillators are non-explosive. Z. Angew. Math. Phys. 47 (1996) 740-759
14. Schenk-Hoppé K.R. Bifurcation scenarios of the noisy Duffing-van der Pol oscillator. Nonlinear Dynam. 11 (1996) 255-274
15. Zeeman E. The unstable behavior of stock exchanges. J. Math. Econom. 1 (1974) 39-49