  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 considered and incorporated. It
is assumed that the instantaneous mean growth rate of foreign exchange rate
price follows an Ornstein-Uhlenbeck process. Dynamic programming method is
employed to study the problem of maximizing the expected exponential utility of
terminal wealth. By soloving the correspoding Hamilton-Jacobi-Bellman
equations, the optimal investment strategies and the value functions are
obtained. Finally, numerical analysis is presented.
