The Optimal Control Problem Of International Investment And Consumer Choice Under The Multiple Impacts

With the continuous development of China’s economy, people’s living s-tandards gradually improved, and a variety of investment channels has become more flexible. When having a certain wealth, people are no longer satisfied in bank savings, bonds and other conservative investments, while turning to the stock and foreign exchange risk investment, as China entered the WTO, investors can choose to overseas industrial investment. In this context, the optimal portfolio theory has aroused the attention of investors.Portfolio theory is to maximize the expected utility of the research in-vestors, we are concerned investors will be part of their wealth for investment, the other part for consumption. In the direction of investment, investors’ wealth by a certain distribution rate to invest in different assets, such as fi-nancial assets and assets of the estate. Considering the investment risk in the previous literature, some only taking into account inflation. and some only consider the exchange rate risk, there is rarely discuss both cases. Practice, for many investors, especially multinational companies are also increasing. Port-folio investment and physical investment can also be a risky assets. In the analysis, the domestic financial assets, investors need to consider the impact of the inflation of its revenue. For the overseas assets of the estate, investors need to consider the impact of exchange rates of their wealth.This article is divided into five chapters: Chapter Ⅰ introduces portfolio theory and its significance, including the development of portfolio theory, overseas industrial investment, the impact of inflation.Chapter Ⅱ firstly giving some introductions to the preview, and then about the problem description which we will solve in this paper and the solution of the problem.Chapter Ⅲ is mainly about in the case of logarithmic utility function,we will give the display solution.Chapter Ⅳ, we pay attention to a special case (Constant Relative Risk Aversion). We will give the optimal strategy expression and discuss several numerical examples.Lastly, Chapter Ⅴ, we review the whole paper and summarize it.