An Ergodic Impulse Control Model with Applications Including the Control of an Exchange Rate∗

We address the problem of controlling a general one-dimensional Itô diffusion within an externally specified bounded interval [A,B] by means of an impulse control process. We minimise a long-term average criterion that penalises deviations of the state process from a given nominal point within this region as well as the use of impulsive control effort. We solve the resulting optimisation problem and we provide an explicit optimal control strategy under general assumptions. The model that we study is motivated by several applications, including the problem of determining an optimal central bank intervention strategy aiming at the control of an exchange rate or an inflation rate, as well as the problem of designing optimal contribution policies in defined benefit pension plans.