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Global Hopf Bifurcation Analysis for a Time-Delayed Model of Asset Prices

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  • Ying Qu
  • Junjie Wei

Abstract

A time-delayed model of speculative asset markets is investigated to discuss the effect of time delay and market fraction of the fundamentalists on the dynamics of asset prices. It proves that a sequence of Hopf bifurcations occurs at the positive equilibrium , the fundamental price of the asset, as the parameters vary. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are determined using normal form method and center manifold theory. Global existence of periodic solutions is established combining a global Hopf bifurcation theorem with a Bendixson's criterion for higher-dimensional ordinary differential equations.

Suggested Citation

  • Ying Qu & Junjie Wei, 2010. "Global Hopf Bifurcation Analysis for a Time-Delayed Model of Asset Prices," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-17, March.
    • Handle: RePEc:hin:jnddns:432821
    DOI: 10.1155/2010/432821
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    References listed on IDEAS

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    1. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. C. H. Hommes, 2001. "Financial markets as nonlinear adaptive evolutionary systems," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 149-167.
    3. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
    4. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2002. "Speculative behaviour and complex asset price dynamics: a global analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 173-197, October.
    5. He, Xue-Zhong & Li, Kai & Wei, Junjie & Zheng, Min, 2009. "Market stability switches in a continuous-time financial market with heterogeneous beliefs," Economic Modelling, Elsevier, vol. 26(6), pages 1432-1442, November.
    6. Dibeh, Ghassan, 2005. "Speculative dynamics in a time-delay model of asset prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 199-208.
    7. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    8. Chiarella, Carl & He, Xue-Zhong, 2003. "Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker," Macroeconomic Dynamics, Cambridge University Press, vol. 7(4), pages 503-536, September.
    9. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
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