Stability in a Discrete-Time Dynamic Model with Delay for a Stock Market

22 Pages Posted: 5 Feb 2012 Last revised: 10 Dec 2012

See all articles by Loretti Dobrescu

Loretti Dobrescu

University of New South Wales, School of Economics

Mihaela Neamtu

West University of Timisoara - Department of Economic, Informatics and Statistics

Dumitru Opris

West University of Timisoara

Date Written: November 19, 2011

Abstract

The 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.

Keywords: price index, mutual fund, stock market, nonlinear dynamic model, Lyapunov exponents

JEL Classification: C58, D53, L1, E32

Suggested Citation

Dobrescu, Loretti Isabella and Neamtu, Mihaela and Opris, Dumitru, Stability in a Discrete-Time Dynamic Model with Delay for a Stock Market (November 19, 2011). UNSW Australian School of Business Research Paper No. 2012ECON11. Available at SSRN: https://ssrn.com/abstract=1987871 or http://dx.doi.org/10.2139/ssrn.1987871

Loretti Isabella Dobrescu (Contact Author)

University of New South Wales, School of Economics ( email )

High Street
Sydney, NSW 2052
Australia

Mihaela Neamtu

West University of Timisoara - Department of Economic, Informatics and Statistics ( email )

Bd. Vasile Parvan nr.4
Timisoara 300223, Timis 330023
Romania

Dumitru Opris

West University of Timisoara ( email )

Bd. Vasile Parvan nr.4
Timisoara 300223, Timis 330023
Romania

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