A Discrete--Delay Dynamic Model for the Stock Market

Loretti Dobrescu, Mihaela Mihaela Neamtu () and Dumitru Opris ()
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Mihaela Mihaela Neamtu: Department of Economic Informatics and Statistics, West University of Timisoara
Dumitru Opris: Department of Applied Mathematics, West University of Timisoara

No 2012-11, Discussion Papers from School of Economics, The University of New South Wales

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. (search for similar items in EconPapers)
JEL-codes: C58 D53 E32 L1 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2011-10
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Persistent link: https://EconPapers.repec.org/RePEc:swe:wpaper:2012-11

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