Entry and exit decision problem with implementation delay

Marius Costeniuc*, Michaela Schnetzer, Luca Taschini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We study investment and disinvestment decisions in situations where there is a time lag d > 0 from the time t when the decision is taken to the time t + d when the decision is implemented. In this paper we apply the probabilistic approach to the combined entry and exit decisions under the Parisian implementation delay. In particular, we prove the independence between Parisian stopping times and a general Brownian motion with drift stopped at the stopping time. Relying on this result, 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).

Original languageEnglish
Pages (from-to)1039-1059
Number of pages21
JournalJournal of Applied Probability
Volume45
Issue number4
DOIs
Publication statusPublished - Dec 2008

Keywords / Materials (for Non-textual outputs)

  • Brownian excursion
  • implementation delay
  • optimal stopping
  • Parisian option
  • Wald's identity

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