A Discrete--Delay Dynamic Model for the Stock Market
AbstractThe time evolution of prices and savings in a stock market is modeled by a discrete-delay nonlinear dynamic system. The proposed model has a unique and unstable steady-state, so its time evolution is determined by the nonlinear effects acting out of the equilibrium. We perform the analysis of the linear approximation through the study of the eigenvalues of the Jacobian matrix in order to characterize the local stability properties and the local bifurcations in the parameter space. If the delay is equal to zero, Lyapunov exponents are calculated. For certain values of the parameters, we prove that the system has a chaotic behaviour. The discrete nonlinear model is associated with a discrete stochastic model. For the liniarization of this model, we establish the conditions for which the mean and quadratic mean values of the state variables are asymptotically stable. Some numerical examples are finally given to justify the theoretical results.
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Bibliographic InfoPaper provided by School of Economics, The University of New South Wales in its series Discussion Papers with number 2012-11.
Length: 22 pages
Date of creation: Oct 2011
Date of revision:
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Web page: http://www.economics.unsw.edu.au/
More information through EDIRC
price index; mutual fund; stock market; nonlinear dynamic model; Lyapunov exponents.;
Find related papers by JEL classification:
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
- D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
- L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gian-Italo Bischi & Vincenzo Valori, 2000. "Nonlinear effects in a discrete-time dynamic model of a stock market," Working Papers - Mathematical Economics 2000-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
- Ana Babus & Casper G. de Vries, 2010.
"Global Stochastic Properties of Dynamic Models and their Linear Approximations,"
Tinbergen Institute Discussion Papers
10-081/2, Tinbergen Institute.
- Babus, Ana & de Vries, Casper G., 2010. "Global stochastic properties of dynamic models and their linear approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 817-824, May.
- Roberto Dieci & Ilaria Foroni & Laura Gardini & Xue-Zhong He, 2005. "Market Mood, Adaptive Beliefs and Asset Price Dynamics," Research Paper Series 162, Quantitative Finance Research Centre, University of Technology, Sydney.
- Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "A Behavioural Asset Pricing Model with a Time-Varying Second Moment," Research Paper Series 141, Quantitative Finance Research Centre, University of Technology, Sydney.
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