Abstract
We formulate a mathematical model for the optimal control of the exchange rate under uncertainty. The control consists of a combination of: 1. 1. (continuous) stochastic control and 2. 2. an impulse control. We give general sufficient conditions for its solution. The results are applied to the following situation: Suppose that a government has two means of influencing the foreign exchange rate of its own currency: 1. 1. At all times t the government can choose the domestic interest rate t −. 2. 2. At selected times the government can intervene in the foreign exchange market by buying or selling large amounts of foreign currency. We assume that the exchange rate is stochastic and that there are given costs involved in these two actions. It is also costly to have an exchange rate which deviates too much from a given central parity m. How does the government apply its two means of influence in order to keep the exchange rate as stable as possible with minimal expected costs? We formulate this problem mathematically as a combined stochastic control (1) and impulse control (2) problem, and we discuss the solution in a specific example.
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call