Optimization Problem For Multinational Assets In A General Jump Model

We consider a market combined by domestic stock and exchange rate, which arethe only risk assets in this market. The price process of these assets are driven bytwo correlative Brown Motion and there exists a common jump process between thesetwo Brown Motion. We discuss the optimization problem when the utility functionin the term of Uexp = exp{?k0x} and also consider the problem how to construct anoptimal portfolio. As introduced in Kohlmannå’ŒXiong(2007), we give a descriptionof this measure (MEMM) as the solution of a backward martingale equation(BME).As an application of BME, we can give the optimal utility and optimal investmentstrategy for investors. Therefore, the conclusion of Kohlmannå’ŒXiong(2007) has beenextended to two-dimensional situation.When parameters are constants, we provide the closed solution of BME. Fur-thermore, we give the closed solution for optimal portfolio which depends only onequations with fixed version and it can be solved with Newton iteration method.