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Entry and Exit Decision Problem with Implementation Delay

Part of: Stochastic processes Sequential methods Markov processes

Published online by Cambridge University Press:  14 July 2016

Marius Costeniuc ,
Michaela Schnetzer  and
Luca Taschini
Marius Costeniuc*
Affiliation:
Swiss Re
Michaela Schnetzer*
Affiliation:
University of Zürich
Luca Taschini*
Affiliation:
University of Zürich
*
∗Postal address: Swiss Re, Zürich, Switzerland. Email address: marius.costeniuc@gmail.com
∗∗Email address: michaela.schnetzer@gmail.com
∗∗∗Postal address: Swiss Banking Institute, University of Zürich, Plattenstrasse 32, 8032 Zürich, Switzerland. Email address: taschini@isb.uzh.ch
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Abstract

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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).

Keywords

Brownian excursionimplementation delayParisian optionoptimal stoppingWald's identity

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J65: Brownian motion 62L15: Optimal stopping
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1039 - 1059
Copyright
Copyright © Applied Probability Trust 2008 

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