Problems of modeling the stability of the financial market as a dynamic system

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Subject. The article addresses the stable functioning of the financial market and its protection against financial crises as the main indicator of financial system’s stability. It considers the history of the issue, enabling to conclude that financial markets are built mainly on the principle of unstable equilibrium in contrast to the more stable equilibrium underlying the commodity markets and industrial production. Objectives. The article attempts to compare well-known stochastic models with dynamic and chaotic systems. Methods. The study employs stochastic modeling (autoregressive conditional heteroscedasticity (ARCH) and generalized autoregressive conditional heteroscedasticity (GARCH) models), investigates methods and approaches to solving some types of differential stochastic equations, in particular, the Ito and Fokker-Planck-Kolmogorov equations. Results. Financial markets are considered within the theory of dynamic systems as an example of a non-linear system. It is extremely difficult to predict the behavior of such a system, precisely because of the non-linearity, which is reduced to random and chaotic processes. Through mathematical transformations, the paper shows that solutions are reduced to multidimensional stochastic volatility models. Conclusions. Stochastic volatility models, despite their relative theoretical elaboration and practical applicability, can lead to dynamic chaos, when there is a vector of asset return, the conditional covariance matrix of which changes over time.