Study On The Consumption-Portfolio Strategy With Risk Aversion

The consumption and investment involve some major problems in the finance market, which the fiance market influences the macroeconomic through. In addition, they have the distinct feedback to the finance market. Most researches of the macroeconomic field are about them. From Arrow, Pratt introduced the concept of risk aversion, these articles about investment with risk aversion are few. As a matter of fact, most investors don't like risk, so it is especially significant to study the behavior of the investors with risk aversion.Thought of the research: (1) Firstly we see through the phenomena to grasp the finance market, then we begin to establish the finance market model and discuss its properties. (2) Secondly the paper separately analyses these problems which are based on the investor's preference to the consumption and portfolio. These questions are the optimal consumption, or the optimal investment, or the optimization of both. (3) We lead the risk aversion into the consumption and investment models to study the optimal consumption plans and portfolio formulas.Methods of the research: (1) The paper mainly depends on the stochastic processes, the stochsatic optimal control theory and the martingale theory, and so on. Establish and analyse the finance market model and the consumption-portfolio model. (2) Most conclusions are obtained by Propositions, Theorems and Corollaries to explain these models in the paper.Based on the discount function /?(i), which is finite measurable, this paper separately discusses the optimal consumption, the optimal investment and the optimization of the consumption and the terminal wealth. Then we get the optimal consumption conditions and the investment formulas. Because most investors don't like risk, so we lead into risk aversion to analyse the consumption-portfolio investment models. At last, we obtain the consumption-portfolio strategies based on the risk aversion coefficients. These models and conclusions are important to understand the fiance market, they provide the theoretical basis for the investor to consume and invest. In addition, the results extend Merton, Karatzas and these articles [8-11].This paper is divided into five chapters. Chapter 1 introduces some mathematical concepts and important theories, chapter 2 is concerned with the finance market model, which discusses the solution and qualities of the model. The analyses focus on the lastthree chapters , they use the stochastic control and the martingale theory to solve the optimal question of the investor: optimal consumption, optimal investment and optimization of utility from terminal wealth. In chapter 3, we get the value function through a way, which is complex, but it shows the detailed information. In chapter 4 and chapter 5, the paper supports a simply method to get the value function, we write both methods in this paper. Further we lead into the risk aversion to analyse portfolio investment model in the paper. Transform the value function to satisfy the HJB differential equation with the coefficient of risk aversion. Particularly, the consumption and security investment tactics are proposed.