Optimal stochastic intervention control with application to the exchange rate

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 deviation from its central parity: i) at all times t, the government can choose the domestic interest rate, and ii) at selected times, the government can intervene in the foreign exchange market. These interventions are costly, but it is also costly to have the exchange rate deviating too much from the central parity. The government will minimize these costs while determining the optimal level of variation for the exchange rate around its parity.

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