The Roles Of Stochastic Factors And Time Delay Of Information On The Financial System

We use methods of statistical physics to investigate the roles of stochastic factors and time delay of information on the financial system. First of all. we give a comprehensive review on the status quo, meaning and related theory of studies with regard to the methods of statistical physics in the financial system. Secondly, the systematic in-depth study on the effects of stochastic factors and time delay of information on the financial system has been done. Based on the Heston model and a cubic nonlinearity to describe stock price dynamics and stock market crash, we mainly discuss the statistical characteristics of stock price in financial crisis, stochastic resonance (SR) and investment portfolio, respectively. The following results show:In the first part of the work, we investigate the influences of information time delay on the stability of stock price, risks and returns of stock investment and roles of extrinsic periodic information on the stability of stock price in financial crisis, respectively. In the first place, after introducing time delay to the Heston model for the volatility, we build a model of stock price dynamics with time delay and analyze the influences of information time delay on the stability of stock price by numerically simulating the mean escape time (MET) of stock price described by Brownian particle. These results indicate that, for the case of strong (or weak) elasticity of demand of stocks, an optimal (or a worst) delay time is associated with the maximum (or minimum) stability of the stock price (SSP); for the case of shorter (or longer) delay time, delay time and cross correlation coefficient between the noise sources play the opposite (or same) role on the SSP. Subsequently, we discuss the roles of the traded time and price point described by delay time and initial position on risks and returns of stock investment. The results show that, for strong (or weak) elasticity of demand of stocks, a certain delay time is related to the minimal (or maximal) risks of stock investment, maximal (or minimal) average stock price returns and strongest (or weakest) stability of stock price returns; the increment of initial position recedes the risks of stock investment, strengthens the average stock price returns and enhances stability of stock price returns. In the final of first part, we introduce the multiplicative periodic function to the Heston model for stock price, establish a collapse model driven by extrinsic periodic infor-mation and investigate the roles of extrinsic periodic information on the stability of stock price by numerically simulating MET. The results demonstrate that, the varying amplitude of extrinsic periodic information induces a maximum in curve of the MET versus the mean reversion of volatility or initial position; a critical phenomena is observed in the behaviors of MET versus the long-run variance or amplitude of volatility fluctuations.In the second part of the work, after the extrinsic and intrinsic periodic in-formation are introduced into the stochastic differential equations of the Heston model for stock price, we build a dynamic model of stock prices driven by periodic information, investigate the SR of the stock prices in finance system and analyze the effects of time delay on SR by focusing on the signal power amplification (S-PA). We observe a phenomenon of reverse-resonance in the behaviors of SPA as a function of the system and external driving parameters, and especially a phe-nomenon of double reverse-resonance in the behavior of SPA versus the amplitude of volatility fluctuations. Concerning the effects of time delay on SR. we observe a critical phenomena induced by time delay in the behaviors of SPA as a function of long-run variance of volatility or cross correlation coefficient between noises.In the final of work, we establish a model for investment portfolio and analyze the roles of investment dispersion and period on risks and returns of investment portfolio. The results demonstrate that, the maximum dispersion of investment portfolio is associated with the minimal investment risks and maximum stability of equity portfolio return, but a worst investment period and an increase of in-vestment period are associated with a maximum investment risk and a decrease of stability of equity portfolio return, respectively.In addition, we compare the probability density function (PDF) of the stock price returns, the PDF of volatility, correlation function of the returns, and the PDF of the escape time of the returns in our model with that obtained from other references or real financial market data, and good agreements are found between them.