| By using the stochastic analysis methods, the optimal consumption and investment portfolio problem under the uncertain environment has become a very important area in financial mathematics. The continuous-time portfolio theory which is first formulated by Merton provides an important theoretical basis for the later researchers. However, due to the financial market is incomplete; it has very important significance in theory and practical to study the optimal portfolio under the additional constraint conditions. In order to build more accurate asset pricing model to describe the actual circumstances, the impact of inflation is considered in this paper. That is, the optimal consumption-investment problem under the impact of inflation is studied in this paper.Firstly, some background information, research significance and present development situations are introduced. Then some elementary knowledge about this paper is presented, including utility function, Brownian motion, Ito formula and stochastic control theory. Then the asset price model under the impact of inflation is researched. At last, using the dynamic programming theory, the explicit solutions are obtained for the CRRA utility function and the HARA utility function. The results show that the terminal wealth expectation is associated with the inflation. When the relationship between the stock volatility and the inflation is negative, the investor should increase the investment proportion for the stock. |
