AUTHORS: Andrey Dmitriev, Vitaly Silchev, Victor Dmitriev

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ABSTRACT: This paper proposes a nonlinear dynamical model of stock market. Dynamical variables of the model are the variation of ask and bid price relative to equilibrium values and difference between numbers of market agents in a-state and p-state. A particular market agent being in a-state has maximum amount of valuable information about financial asset and has minimum information being in p-state. This model explains the impossibility of existence of an equilibrium state of the market, shows the presence of deterministic chaos in a stock market and fractal financial time series. The results of the nonlinear dynamical analysis and statistical analysis of the empirical financial time series are presented. We show the results of nonlinear analysis for the model as an open nonequilibrium system, as well as comparison with empirical results.

KEYWORDS: stock market model, stock market indexes, deterministic chaos, financial time series, correlation dimension, fractal dimension, 1/f noise, long memory, q-Gaussian distribution.

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WSEAS Transactions on Business and Economics, ISSN / E-ISSN: 1109-9526 / 2224-2899, Volume 14, 2017, Art. #33, pp. 311-321


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