Nonlinear stochastic exclusion financial dynamics modeling and complexity behaviors

Abstract

In attempt to reproduce and investigate nonlinear dynamics of financial markets, a new random agent-based financial price dynamics is developed and investigated by stochastic exclusion process. The exclusion process, one of Markov interacting processes, is firstly introduced to imitate the trading interactions among the investing agents in this work and to explain various statistical facts found in financial data. To better understand the fluctuation complexity properties of the proposed model, the complex analyses of random logarithmic price return series are preformed, including power-law distribution, Lempel–Ziv complexity, correlation dimension analysis, maximum Lyapunov exponent, mean Lyapunov exponents and Kolmogorov–Sinai entropy density. In order to verify the rationality of the model, the corresponding analyses of real return series are also studied for comparison. The empirical research reveals that this financial model can reproduce similar statistical behaviors, power-law distribution of returns, complexity and chaotic features of returns for real stock markets.