Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Bifurcation analysis of a single-group asset flow model


Authors: H. Merdan, G. Caginalp and W. C. Troy
Journal: Quart. Appl. Math. 74 (2016), 275-296
MSC (2010): Primary 91B25, 91B26, 91B50, 34D20, 37G15; Secondary 91G80, 91G99, 34C60, 37N40
DOI: https://doi.org/10.1090/qam/1418
Published electronically: March 21, 2016
MathSciNet review: 3505604
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Abstract: We study the stability and Hopf bifurcation analysis of an asset pricing model that is based on the model introduced by Caginalp and Balenovich, under the assumption of a fixed amount of cash and stock in the system. First, we analyze stability of equilibrium points. Choosing the momentum coefficient as a bifurcation parameter, we also show that Hopf bifurcation occurs when the bifurcation parameter passes through a critical value. Analytical results are supported by numerical simulations. A key conclusion for economics and finance is the existence of periodic solutions in the absence of exogenous factors for an interval of the bifurcation parameter, which is the trend-based (or momentum) coefficient.


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Additional Information

H. Merdan
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 — and — Department of Mathematics, TOBB University of Economics and Technology, 06560-Ankara, Turkey
Address at time of publication: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: merdan@pitt.edu, merdan@etu.edu.tr

G. Caginalp
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: caginalp@pitt.edu

W. C. Troy
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: troy@math.pitt.edu

DOI: https://doi.org/10.1090/qam/1418
Keywords: Asset price dynamics, stability of price dynamics, Hopf bifurcation, price trend, momentum, market dynamics, liquidity, periodic solutions
Received by editor(s): August 15, 2014
Published electronically: March 21, 2016
Additional Notes: The first author was supported by TUBITAK (The Scientific and Technological Research Council of Turkey)
Article copyright: © Copyright 2016 Brown University


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