One Kind Of Optimal Problem Of Consumption And Investment Profolio In The Security Market And Entity Project

With the improvement of living standards of our country,how to realize the wealth’s value preservation and appreciation has already become the focus of people.As we all know,though bank savings and bonds have strong security,our revenue will be low as low interest rates,even the revenue has not kept pace with inflation.As a result,in order to achieve the rapid growth of asset,people are willing to invest risky assets.However,investment is full of uncertainties with high risk.Moreover any careless asset investment maybe lose all money.So how to avoid investment trap and how to choose assets with low risk and high yield has become a tough problem for broad investors.Actually,we can turn it into optimal portfolio selection problem in the area of financial mathematics.On the basis of balancing risk and return of investments,we should find the optimal investment strategies to reduce risk and maximize the expected utility of asset.According to optimal portfolio theory,firstly,we consider that the wealth of inventors is divided into two sections: one is that inventing a real project,one is that investing the securities markets.Then,based on inflation,we solve the optimal portfolio (x~*(t),c~*(t)),and get explicit expressions.The full text is divided into six chapters:(1)in the first chapter,we analyze background and meaning that this research problem puts forward,including development process of the theory of financial mathematics,classical models of portfolio theories,domestic investment for real projects,and the influence of inlation.(2)the second chapter is about the inttroduction for some basic theories,which will be used in this research,including the Brownian motion and its characteristics,the It(?) process,the theory of stochastic optimal control.(3)the third chapter is mainly about the theoretical analysis and the model resolution,getting the theoretical solution of optimal investment and consumption strategy (x~*(t),c~*(t)).What’s more,the paper uses relative risk aversion measure to discuss the actual meaning of the model.(4)In the forth chapter,the paper addresses the explicit solution of HJB equation.Under situations of logarithmic utility function and “CRRA”,we solve the HJB equation and get the explicit expression of optimal investment and consumption strategy.(5)In the fifth chapter of this paper,we give several specific numerical examples,and how the percentage of optimal wealth investment*x affects the rates of return on investment for the domestic real projects and the securities markets.(6)the sixth chapter is mainly about a summary of the research results and the development direction in the future.