Two State Stochastic Control Models with Fix Costs

In this document I analyze a stochastic control model with a two dimensional state variable and fix costs. To illustrate the results, I study a simple Central Bank decision model with multiple objectives and restricted number of policy instruments in which in absence of intervention, objective variables follow diffusion processes. I present the solution to a baseline model in which both state variables can be controlled separately and compared them to the case in which there is only one control variable to change both states. I solve the models numerically and suggest a characterization of the respective inaction and control regions