Entry and Exit Decision Problem with Implementation Delay

Abstract

We study investment and disinvestment decisions in situations where there is a time lag 0 from the time t when the decision is taken to the time when the decision is implemented. Applying the probabilistic approach to the combined entry and exit decisions under the Parisian implementation delay, we solve the constrained maximization problem, obtaining an analytic solution to the optimal "starting" and "stopping" levels. We compare our results with the instantaneous entry and exit situation, and show that an increase in the uncertainty of the underlying process hastens the decision to invest or disinvest, extending a result of Bar-Ilan and Strange (1996).

Keywords: Brownian excursion, Implementation Delay, Parisian Option, Optimal Stopping, Wald's Identity

JEL Classification: C60, C61, C65, G13