A two-dimensional stochastic model for the interest rate and the inflation rate is suggested. A control process, entering the dynamics of the interest rate additively, represents the action of the Central Bank. Inflation targeting while stimulating the economy, is achieved by minimizing a cost functional involving all three processes. This is a singular stochastic optimal control problem.
We discuss the analytic solution, which depends on an unknown but smooth free boundary, we fit the model to some Canadian data, and we povide a numerical approximation to the solution of the control problem.