Abstract: In this paper, we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model. Investment in the foreign market is allowed, and therefore, the foreign exchange rate model is incorporated. Under the allowing of selling and borrowing, the problem of maximizing the expected exponential utility of terminal wealth is studied. By solving the corresponding Hamilton-Jacobi-Bellman equations, the optimal investment strategies and value functions are obtained. Finally, numerical analysis is presented.