We consider an open-economy model with the Calvo-type sticky prices. We mainly analyze the situation in which the monetary authority in each country cooperates so as to maximize the world welfare. In the case where the zero lower bound (ZLB) on nominal interest rates never binds, the optimal inflation targeting rule in our open-economy model has exactly the same form as in the closed-economy model. This is not the case, however, when the ZLB may bind. The optimal paths are characterized in such a situation. In contrast with what has been suggested in the existing literature, the optimal paths of the nominal exchange rate in our model typically exhibit appreciation of the currency of the country where the ZLB binds.