Managing inflation: a control problem

The central bank´s action on the nominal interest rate r(t), aiming to contain the rate of inflation π(t), is modeled as a control problem in which the two dimensional state process (r,π) is driven by a diffusion process and the action of the bank is represented by a bounded variation process k that enters the dynamics of r additively. A variational inequality for the value function is derived and the regularity of the corresponding free boundary is studied. This allows the construction of an optimal policy kˆ; it is shown that the optimal state process is a diffusion reflected at the free boundary