The Study Of Dynamic Properties For A Continuous Asset-pricing Model

The asset pricing theory was originated form the U.S. capital market, which is one of the contents investigating modern financial theory. As we know, the Wall Street’s twice "financial revolution" is related to the use of the asset pricing theory. In the early 1950s, Markowitz put forward portfolio theory, making the rate of return on assets mean and variance as selected objects, without regarding to the individual utility function. Thus investors can only make the mean and variance of the asset returns as selected targets. Before 1950s, it is recognized that the financial asset pricing theory is not thought to form certain systems.Under certain assumptions, the asset pricing model can be described by a second order linear differential equation. The solutions of the equation represent the equilibrium or no-arbitrage economic conditions. In this paper, considering some economic situations.we establish a continuous time of one-dimensional asset pricing model, which is a nonlinear model. The nonlinear model extends the linear model discussed by Chen (2008). It is shown that our model represents more real economic situations and has several dynamic properties. The background of the capital asset pricing theory is presented in chapter 1. In chapter 2, the Ito’s lemma and Euler equations are used to deduce a second-order nonlinear price dividend equation. The nonlinear model is proved to be a equivalent economic model under some conditions. The existence and uniqueness of solutions for the equivalent model are investigated. Several concrete examples are given in Chapter 3 to show that existence of solution for the price dividend equation.