The Construction And Qualitative Research Of Differential Equation Model Of Interest Rate-Circulating Amount In Financial Market

This thesis constructs a series of differential equation models reflecting the interest rate changes in the financial system for various financial backgrounds. It also studies the laws of changes of interest rate and the stability of financial market by applying the stability theory of differential equation. The study with an elaborate insight is made of the behavior of the model solutions based upon the systematic application of modern differential equation theories including functional differential equation and impulsive differential equation. The research results bring to light some inherent laws in financial field and interpret and predict the stability of financial market. This research offers a new thinking pattern for the development of financial theories and thus is of vital theoretical significance. Meanwhile, the research result offers a new basis for the macro-decision-making in financial field and therefore is of some practical significance.In the first section of Chapter 2, the differential equation model of Interest Rate-Amount of Circulating Fund in a closed system is constructed, and it is proved that the sum of the weighted interest rates of all nodes is a constant, namely, Equilibrium Principle of Interest Rate of Financial Network and that the limit of the interest rates of each node is the average interest rates of the whole network. In the second section of Chapter 2, the fact that the essential interest rates of all nodes differ from each other is discussed, a non-homogeneous differential equation model of interest Rate-Amount of Circulating Fund is established, and it is proved that the sum of the weighted interest rates of each node in the financial network still remains a constant and that the difference of the instant interest rates between two nodes will finally approach the difference between their basic interest rates. In the third section of Chapter 2, the differential equation model of Interest Rate-Amount of Circulating Fund in an open system is studied, the laws of changes of interest rate are taken into account when fund is injected into or withdrawn from the node or when fund is injected into the network or withdrawn from the network, and the stability of equilibrium solution is proved based upon Lyapunov stability theory. In the last, the equation model of interest Rate-Amount of Circulating Fund in the financial network with time delay is studied, and a necessary and sufficient condition for theexistence of periodic solution is obtained to the Interest Rate-Amount of Circulating Fund equation with delay.The third chapter of the thesis makes a study of the equation of Interest Rate-Amount, of Circulating Fund on limited occasions of sudden events, proves that the network average interest rates of different time periods are also different and change with the impulsive conditions, and makes clear the relationship between the network average interest rates of two neighboring time periods. As far as every node in the network is concerned, its instant interest rate will tend to, in the end, at the sum of the basic interest rate of every node and the growth rate of the network. Moreover, considering that the proportional coefficients at which interest rates change with the Amount of Circulating Fund depend on time, the non-autonomous Interest Rate-Amount of Circulating Fund equatoin is constructed and an elaborate study is made of the nature of its solution in normal cases and in the cases of impulse disturbance.In the fourth chapter of the thesis, a study is made of the equation of Interest Rate-Amount of Circulating Fund with infinite impulse disturbance in an open network. As far as linear and non-linear impulse disturbances are concerned, the conditions on which the system still remains stable under impulse disturbance and the conditions on which impulse disturbance leads to the changes of the stability of the system are discussed.