Stability And Control Of Financial System With Delay

With the development of economy in China, our country will have greater developmentand breakthrough in financial market. Facing many opportunities and challenges, financialmarket is in urgent need scientific theory as guidance. Through the observation of manyphenomena in financial market, we discuss a two-dimensional asset price system with delayby impulsive control, a three-dimensional stock price system with two delays by impulsivecontrol, and construct a five-dimensional asset price-profit model with multi delays, exploringthe phenomena of the financial market asset prices from different points of view.Research shows that two-dimensional asset price system with delay by impulsive controland three-dimensional stock price system with two delays by impulsive control, five-dimensional asset price-profit model with multi delays showed the respective superiority indifferent methods to explore the problem. This study mainly includes the following aspects:(1) On the basis of the original asset price system, through the further discussion on theimpulsive control stability, we discuss a two dimensional continuous asset price impulsivesystem with delay. Firstly, aim at traders’ parameters and delay, this paper analyzes thecharacteristics of asset price impulsive system. Secondly, by constructing a Lyapunovfunction, we present the conservative conditions for global exponential stability of theimpulsive system.To the two-dimensional impulsive system, we give numerical simulation, and thesimulation results are the numerical analysis. The simulation results are in consistent with thetheoretical analysis, which explains the application value of asset price impulsive model infinancial market.(2) Considering the conditions in the financial markets, the fundamental price closelycontacts with markets excess demand, and depends on the excess demand to make someadjustments. On the basis of the original asset price system, through the further discussion onthe impulsive control stability, we discuss a three-dimensional continuous stock priceimpulsive system with delays. The same is that firstly, aiming at traders’ parameters anddelays, this paper analyzes the characteristics of stock price impulsive system. Secondly, byconstructing a Lyapunov function, we present the conservative conditions for globalexponential stability of the impulsive system.To the three-dimensional impulsive system, we give numerical simulation, and thesimulation results are the numerical analysis. The simulation results are in consistent with thetheoretical analysis, which explains the application value of stock price impulsive model inthe search process of financial market price stability.(3) Considering the complexity of our financial market, and there exist stock prices andprofits, we propose and study a five-dimensional price-profit model with multi delays. Themodel optimizes the discrete model with different structure, and at the same time, accordingto the profit, adaptive behaviors on the fundamental traders and trend followers under thefluctuant fundamental price is considered. This paper studies the characteristic equation oflinear approximate differential system with delay, and gives the analysis of parameterbifurcation, the conditions of the bifurcation behavior and local stability are found. The theoretical results show not only the different behavior of fundamentalists and trends, but alsothe fluctuant fundamental price will have effects on market instability.For the complex price-profit system with multi delays, we construct numericalsimulation, and the simulation results are analyzed. The simulation results demonstrate thecharacteristic of the above model, which indicates that the practical value of this model indescribing the stability dynamic of the financial market price.