Market stability switches in a continuous-time financial market with heterogeneous beliefs |
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Authors: | Xue-Zhong He Kai Li Junjie Wei Min Zheng |
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Affiliation: | aSchool of Finance and Economics, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia;bDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China |
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Abstract: | By considering a financial market of fundamentalists and trend followers in which the price trend of trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examine the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. These interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, sufficient conditions on the stability and global existence of the periodic solution are obtained. |
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Keywords: | Asset price Fundamentalists Trend followers Delay differential equations Stability Bifurcations |
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