The Qualitative Analysis Of Discrete Mathematical Models On The Rate Of Return In Financial Market

This thesis mainly concerns the stability of the rate of return in the financial market by applying the basic theories and methods of difference equations (including the theory of delay difference equations and the theory of impulsive difference equations). Corresponding to various different financial backgrounds, a series of difference equation models are built up to reveal the stability and laws of the rate of return in the financial network. The asymptotical behaviors and periodic oscillations have been studied by applying the modern theories of difference equations. These results clarify some essential regulations of the rate of return in the financial fields and can be used to estimate and predict the stability of the financial market. Also, these researches are of importance to the development and completeness of the financial theory and can provide a kind of new basis for the macro1 view decision in financial field.In Chapter 2, a series of discrete rate of return-amount of circulating fund models (discrete RRACF model) are built up under various different financial backgrounds. More specifically, concerning the relatively closed financial network, we build up a basic discrete RRACF model reflecting the law of instant rates of return of each node in the financial network. Since every financial network is open, we build up a model corresponding to the open financial network. Usually, getting the profit need some time after investing. So we improve the rate of return-amount of circulating fund equation and build up a new discrete equation with delay. All of the three equations are established in the case of the normal situation. However, many abrupt phenomena can cause the wave of a financial market. Duo to this, we build up another equation concerning the rate of returns and the amount of circulating fund with impulsive terms.Chapter 3- Chapter 6 mainly deals with the detailed discussion on the equations established in Chapter 2. By applying the modern qualitative theory and stability theory of difference equations, we study the stability of the equilibrium, the existence and multiplicity of periodic solutions and solutions of boundary value problems etc. In Chapter 3, we obtain the Equilibrium Principle of the Rate Return in Financial Market, that is, the weighted sum of instant rate of return of nodes in the network is a constant. For each node, its instant rate of return tends to the average rate of return of whole network; Chapter 4 deals with the discrete rate of...