Entry-exit decisions with implementation delay under uncertainty

TL;DR

This paper analyzes optimal entry and exit timing for projects with implementation delays under uncertainty, providing explicit formulas and addressing cases with negative total costs, which are common in practice.

Contribution

It extends existing models by removing the nonnegative cost restriction and characterizing dual trigger points for entry decisions in such scenarios.

Findings

Derived closed-form solutions for optimal entry and exit times.

Identified two trigger points for entry when total costs are negative.

Showed that immediate entry and exit is not optimal even if arbitrage exists.

Abstract

We employ a natural method from the perspective of the optimal stopping theory to analyze entry-exit decisions with implementation delay of a project, and provide closed expressions for optimal entry decision times, optimal exit decision times and the maximal expected present value from the project. The results in conventional research were obtained under the restriction that the sum of the entry cost and the exit cost is nonnegative. In practice, we usually meet this sum is negative, so it is necessary to remove the restriction. If the sum is negative, there may exist two price triggers of entry decision, which does not happen when the sum is nonnegative, and it is not optimal to enter and then immediately exit the project even though it is an arbitrage opportunity.