An Investment Model with Switching Costs and the Option to Abandon

TL;DR

This paper presents a comprehensive analysis of an investment model with switching costs and abandonment options, providing explicit solutions and revealing complex optimal strategies in stochastic environments.

Contribution

It introduces a complete solution to a stochastic control problem involving switching and abandonment, with explicit strategies and rich structural insights.

Findings

Optimal strategies can take up to eight different forms.

Explicit solutions are derived for the complex impulse control problem.

The model captures the impact of switching costs and abandonment on investment decisions.

Abstract

We develop a complete analysis of a general entry-exit-scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic indicator such as the price of or the demand for the project's output commodity. We assume that the investment project can operate in two modes, an "open" one and a "closed" one. The transitions from one operating mode to the other one are costly and immediate, and form a sequence of decisions made by the project's management. We also assume that the project can be permanently abandoned at a discretionary time and at a constant sunk cost. The objective of the project's management is to maximise the expected discounted payoff resulting from the project's management over all switching and abandonment strategies. We derive the explicit solution to this stochastic control problem that involves impulse control as well as discretionary stopping. It turns out that this has a rather rich structure and the optimal strategy can take eight qualitatively different forms, depending on the problems data.