We model an impulse control problem when the controller's action affects the state as well as the dynamics of the state process for a random amount of time. We apply our model to solve a central bank intervention problem in the foreign exchange market when the market observes and reacts to the...

We formulate a mathematical model for the optimal control of the exchange rate. The control consists of a stochastic control, and an impulse control. We give general sufficient conditions for its solution. We consider a government that has two means of avoiding the foreign exchange rate...