The Optimal Portfolio Problem Under The Impact Of Inflation

In our realistic life, when we get fund, we will use a part of it to update consumption, use the rest to investment. According to the different style of in-vestment, we can choose to invest in risky assets or in risk-free assets. In the study of portfolio optimization problem, an important problem is when investor put his money into the bank account (or a bond) and a stock, how to divide his money to get the best result in the case of considering consumption rate.To solve this kind of problem, the dynamic programming method and mar-tingale method are two main methods. But in most of papers, they only consider the stock as the risk asset. Few people consider the usual case where the real project can be seen as a risk asset. However as we know, according to the differ-ent objects, people could have two kinds of investing activity. People can invest in a real project directly or indirectly in virtual economy, such as deposit at bank, buying some stock, bond, fund, future of option.This paper is mainly about the portfolio choice with considering the effect of inflation when the investor invests into a real project. The method which we will use is stochastic dynamic programming.The first part of this paper is mainly about the introduction to the back-ground of the portfolio problem, including the significance of modern portfolio theory, its development and the effect that inflation has taken to production, liv-ing and investment strategy.The second part is mainly about some introductions to the preview.The third part is mainly about the problem description which we will solve in this paper and the solution of the problem.In the fourth part, we pay attention to a special case. We get the explicit solution for this case. In the end, we discuss several numerical example, and give an economic explanation.Lastly, in the fifth part of the paper, we review the whole paper and sum-marize it.