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Dynamical analysis for a model of asset prices with two delays

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  • Wang, Luxuan
  • Niu, Ben
  • Wei, Junjie

Abstract

This paper provides a new perspective to understand the mechanism on the market stability or oscillation by investigating a two-dimensional asset price model with two delays. Stability conditions and the existence of Hopf bifurcation are obtained by investigating the characteristic equation. Then an explicit algorithm for determining the criticality of Hopf bifurcation and stability of the bifurcating solutions is derived, using the center manifold reduction method. The global continuation of bifurcating periodic solutions is detected using a global Hopf bifurcation theorem. It is found that delay may induce supercritical Hopf bifurcations, hence bring oscillation into the asset price model. Moreover, when time delay gets larger, the period of oscillation also increases. Finally, some numerical illustrations with Matlab and DDE-Biftool are carried out to support the theoretical analysis.

Suggested Citation

  • Wang, Luxuan & Niu, Ben & Wei, Junjie, 2016. "Dynamical analysis for a model of asset prices with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 297-313.
    • Handle: RePEc:eee:phsmap:v:447:y:2016:i:c:p:297-313
    DOI: 10.1016/j.physa.2015.12.054
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    1. Chiarella, Carl & He, Xue-Zhong & Wang, Duo & Zheng, Min, 2008. "The stochastic bifurcation behaviour of speculative financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3837-3846.
    2. 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.
    3. Dellas, Harris & Hess, Martin, 2005. "Financial development and stock returns: A cross-country analysis," Journal of International Money and Finance, Elsevier, vol. 24(6), pages 891-912, October.
    4. 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.
    5. 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.
    6. Serwa, Dobromil & Bohl, Martin T., 2005. "Financial contagion vulnerability and resistance: A comparison of European stock markets," Economic Systems, Elsevier, vol. 29(3), pages 344-362, September.
    7. Li, Kai & Wei, Junjie, 2009. "Stability and Hopf bifurcation analysis of a prey–predator system with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2606-2613.
    8. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
    9. Westerhoff, Frank, 2003. "Speculative markets and the effectiveness of price limits," Journal of Economic Dynamics and Control, Elsevier, vol. 28(3), pages 493-508, December.
    10. Dibeh, Ghassan, 2007. "Contagion effects in a chartist–fundamentalist model with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 52-57.
    11. Maskawa, Jun-ichi, 2003. "Multivariate Markov chain modeling for stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 317-322.
    12. Martens, Martin & Poon, Ser-Huang, 2001. "Returns synchronization and daily correlation dynamics between international stock markets," Journal of Banking & Finance, Elsevier, vol. 25(10), pages 1805-1827, October.
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