Application of the Nonlinear Oscillations Theory to the Study of Non-equilibrium Financial Market

Financial Assets and Investing. 2016. Vol. 7. No. 3. P. 5–19.

Марков Н. В., Дмитриев В. А., Мальцева С. В., Дмитриев А. В.

The research deals with the construction, implementation and analysis of the model of the non-equilibrium financial market using econophysical approach and the theory of nonlinear oscillations. We used the scaled variation of supply and demand prices and elasticity of these two variables as dynamic variables in the simulation of the non-equilibrium financial market. View of the dynamic variables data was determined based on the strength of econophysical prerequisites using the model of hydrodynamic type. As a result, we found that the non-equilibrium market can be described with a good degree of accuracy with oscillator models with nonlinear rigidity and a self-oscillating system with inertial self-excitation. The most important states of model of oscillation non-equilibrium model of the market were found, including the appearance of chaos and its mechanisms. We have made the calculations of the correlation dimension for the financial time series. The results show that all observed time series have a clearly defined chaotic dynamic nature.

Ключевые слова: financial market, financial time series, nonlinear oscillations, Lorenz system, ask price, bid price, correlation dimension, non-equilibrium system, low-dimensional chaos