Optimization Problems In Cross-currency Financial Market

In the paper, the optimization problem of consumption/investment is considered under cross-currency financial market condition,for the agent whose action cannot affect the market prices and whose intention is to maximize total expected utility of both consumption and terminal wealth. In the section I(Chapter 1,2),we introduce some great jobs of mathematician in the area. However, most of the papers are based on the one country condition. We change the condition and add a foreign market into the model to form a cross-currency market.In section II,we consider the consumption/investment problem under complete market and cross-currency market conditions. The solution to the problem we used is to represent the price of assets in the foreign market in domestic currency. Then we can treat the problem as the usual consumption/investment problem. And we also discuss the impact of currency exchange on the consumption/investment.In section II,we consider the consumption/investment problem under incomplete market and cross-currency market conditions. We treat the incomplete market as a specific situation of the constrained market. Then we use the method of auxiliary market to solve the problem.