Long-term Optimal Real Investment Strategies in the Presence of Adjustment Costs

We consider the problem of determining in a dynamical way the optimal capacity level of an investment project that operates within a random economic environment. In particular, we consider an investment project that yields a payoff at a rate that depends on its installed capacity level and on a random economic indicator such as, for instance, the price of the project’s output commodity. We model the economic indicator by a one-dimensional ergodic Itô diffusion. At any time, the capacity level can be increased or decreased at given proportional costs. The aim is to maximise the long-term average profit, which takes the form of an ergodic optimisation criterion. The associated Hamilton-Jacobi-Bellman equation is a two-dimensional differential equation that we solve explicitly. We characterise completely an optimal strategy.