Stochastic Interactive Financial Systems With Fluctuation Behavior And Complexity Analysis

Based on three different statistical physical models and different dynamic struc-tures,this paper constructs stock price dynamic models in the financial markets and proposes new statistics to obtain the fluctuation characteristics of the financial time se-ries.By using the non-linear statistical analysis method,we analyze and compare the characteristics of volatility and complexity of the real market and simulated data from the model.Besides,this paper studies the volatility relationship between the oil market and the stock market.The specific structure is as follows:In chapter 1,Introduction of the research background,the main theoretical basis,the research content and the innovation of the paper.In chapter 2,a micro-financial price model based on a three-dimensional Potts in-teractive particle model is introduced to study the nonlinear complexity behavior of the stock market.The three-dimensional Potts model extends the two-dimensional Potts model from a plane to three-dimensional and is used to describe the magnetic interac-tion between particles in a cubic lattice.To study the complexity of the actual financial market and the three-dimensional Potts financial price model,a new random coarse-grained Lempel-Ziv complexity method is proposed to study the complexity of the return time series,the absolute return series,and the return series under a random time scale.Then the composite multiscale entropy(CMSE)method which is an extension of multiscale entropy is combined with the empirical mode decomposition and is applied to the intrinsic mode functions(IMFs)and the corresponding shuffled data to study the complexity behaviors under a different scale.The empirical results indicate that the 3D financial model is feasible to a certain extent.In chapter 3,a new agent-based financial price model is established on the per-colation system on Sierpinski gasket lattice to reproduce the statistical characteristics of financial markets.Sierpinski gasket lattice is a fractal-like graph.According to the theory of percolation on the Sierpinski gasket,the particles on the same cluster corre-spond to investors who hold the same investment attitude in the financial market.The percolation process is the process of exchanging information.To prove the feasibility of the proposed model and study the statistical characteristics,two new nonlinear statistics maximum and average monotonic volatility duration are introduced in this work for the first time,which describes the trend of the volatility of return time series in financial markets.Furthermore,a new method CMCID is proposed to measure the synchroniza-tion and similarity behaviors of return volatility duration in multiscale,the results show that the pairs of real data and simulated data have synchronization,and the synchro-nization becomes stronger when the scale increases.And the power-law distribution is employed to investigate the corresponding statistical properties,which shows that the monotonic volatility duration series of the proposed model shares a common power-law distribution with real markets.The empirical results show that the simulated series from the financial model and the historical data share common statistical properties,which indicate that the proposed model is reasonable in terms of volatility behavior.In chapter 4,it is well known that financial markets contain a large number of interacting particles.The way that information exchange in the previous two chapters is the process of interacting between particles,such as magnetic fields or percolation processes,which caused dynamic changes in financial prices.Different from that,in this chapter a financial price model is established through a stochastic finite-range exclusion process.An exclusive process is a Markov motion with a conserved number of particles on a countable set.According to a certain rule,the particle jumps to another site with a certain probability.When the particle changes the site,it is considered that it has given up the state of the original site and holds the new state in the new site.The change of state corresponds to the change of investor's investment attitude in the financial market.To measure the volatility of the financial return series,a novel statistic called maximum monotonic volatility rate is put forward to measure the speed of the monotonic volatility of returns.Meanwhile,the average monotonic volatility duration of returns is also investigated,which can reflect the average volatility level.To verify the rationality of the model,matching energy analysis that can detect chaos and complexity in nonlinear time series combined with empirical mode decomposition is applied to study the new statistics.The proposed financial model and real markets both show multifractal and anti-correlation for average monotonic volatility series by MFDFA method.The results display that the model is feasible with respect to the above volatility analyses.In chapter 5,the linkages and the degree of synchronization between the crude oil market and the stock market are investigated.The nonlinear cross-analysis method CR-P of bivariate data is used to study the probability distribution of occurrence of similar states and the time span of occurrence of synchronization dynamics for crude oil return series and stock return series.Further,a composite multiscale complexity invariance distance is introduced to measure the similarity of complexity between crude oil mar-kets and stock markets.The results of this study show that there is a synchronization in the crude oil markets and stock markets,and those two systems have similar complexity from composite multiscale perspective.In chapter 6,summarization of the research results of the paper.