Irreversible investment with fixed adjustment costs: a stochastic impulse control approach

TL;DR

This paper models irreversible investment decisions with fixed costs using stochastic impulse control, proving the value function's properties and analyzing optimal strategies through theoretical and numerical methods.

Contribution

It introduces a novel approach combining viscosity solutions and semiconvexity to characterize the value function and optimal control in irreversible investment models.

Findings

Value function is a classical solution to the quasi-variational inequality.

Characterization of continuation and action regions for optimal control.

Numerical analysis of parameter sensitivity in the linear case.

Abstract

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to the associated quasi-variational inequality. This enables us to characterize the structure of the continuation and action regions and construct an optimal control. Finally, we focus on the linear case, discussing, by a numerical analysis, the sensitivity of the solution with respect to the relevant parameters of the problem.