Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 310471, 30 pages
doi:10.1155/2009/310471
Research Article

The Emergence of Bull and Bear Dynamics in a Nonlinear Model of Interacting Markets

Fabio Tramontana,1 Laura Gardini,2 Roberto Dieci,3 and Frank Westerhoff4

1Dipartimento di Economia, Università Politecnica delle Marche, 60121 Ancona, Italy
2Dipartimento di Economia e Metodi Quantitativi, Università degli Studi di Urbino, 61029 Urbino, Italy
3Dipartimento di Matematica per le Scienze Economiche e Sociali, Università di Bologna, 40126 Bologna, Italy
4Department of Economics, University of Bamberg, 96047 Bamberg, Germany

Received 29 August 2008; Revised 8 February 2009; Accepted 27 March 2009

Academic Editor: Xue- He

Copyright © 2009 Fabio Tramontana et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We develop a three-dimensional nonlinear dynamic model in which the stock markets of two countries are linked through the foreign exchange market. Connections are due to the trading activity of heterogeneous speculators. Using analytical and numerical tools, we seek to explore how the coupling of the markets may affect the emergence of bull and bear market dynamics. The dimension of the model can be reduced by restricting investors' trading activity, which enables the dynamic analysis to be performed stepwise, from low-dimensional cases up to the full three-dimensional model. In our paper we focus mainly on the dynamics of the one- and two- dimensional cases, with numerical experiments and some analytical results, and also show that the main features persist in the three-dimensional model.