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Entry and Exit Decision Problem with Implementation Delay

Part of: Sequential methods Stochastic processes 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 

References

Avellaneda, M. and Wu, L. (1999). Pricing Parisian-style options with a lattice method. Internat. J. Theoret. Appl. Finance 2, 1–16.Google Scholar
Bar-Ilan, A. and Strange, C. (1996). Investment lags. Amer. Econom. Rev. 86, 610–622.Google Scholar
Black, F. and Scholes, M. S. (1973). The pricing of options and corporate liabilities. J. Political Econom. 7, 637–654.Google Scholar
Brekke, K. A. and Øksendal, B. (1994). Optimal switching in an economic activity under uncertainty. SIAM J. Control Optimization 32, 1021–1036.Google Scholar
Brennan, M. J. and Schwartz, E. S. (1985). Evaluating natural resource investments. J. Business 58, 135–157.Google Scholar
Chesney, M., Jeanblanc, M. and Yor, M. (1997). Brownian excursions and Parisian barrier options. Adv. Appl. Prob. 29, 165–184.Google Scholar
Deng, S. and Oren, S. S. (2003). Incorporating operational characteristics and start-up costs in option-based valuation of power generation capacity. Prob. Eng. Inf. Sci. 17, 155–181.CrossRefGoogle Scholar
Dixit, A. (1989). Entry and exit decisions under uncertainty. J. Political Econom. 97, 620–638.Google Scholar
Dixit, A. K. and Pindyck, R. S. (1994). Investment Under Uncertainty. Princeton University Press.Google Scholar
Duckworth, K. J. and Zervos, M. (2000). An investment model with entry and exit decisions. J. Appl. Prob. 37, 547–559.Google Scholar
Gauthier, L. and Morellec, E. (2000). Investment under uncertainty with implementation delay. In New Developments and Applications in Real Options. Oxford University Press.Google Scholar
Haber, R. J., Schonbucker, P. J. and Wilmott, P. (1999). Pricing Parisian options. J. Derivatives 6, 71–79.Google Scholar
Hamadène, S. and Jeanblanc, M. (2007). On the starting and stopping problem: application in reversible investments. Math. Operat. Res. 32, 182–192.Google Scholar
Harris, M. and Raviv, A. (1996). The capital budgeting process: incentives and information. J. Finance 51, 1139–1174.Google Scholar
Knudsen, T. S., Meister, B. and Zervos, M. (1999). On the relationship of the dynamic programming approach and the contingent claim approach to asset valuation. Finance Stoch. 3, 433–449.CrossRefGoogle Scholar
Majd, S. and Pindyck, R. S. (1987). Time to build, option value, and investment decisions. J. Financial Econom. 18, 7–27.Google Scholar
McDonald, R. and Siegel, D. (1986). The value of waiting to invest. Quart. J. Econom. 101, 707–728.Google Scholar
Merton, R. C. (1973). Theory of rational option pricing. Bell J. Econom. 4, 141–183.Google Scholar
Øksendal, B. (2005). Optimal stopping with delayed information. Stoch. Dyn. 5, 271–280.Google Scholar
Pindyck, R. S. (1991). Irreversibility, uncertainty, and investment. J. Econom. Literature 29, 1110–1148.Google Scholar
Pindyck, R. S. (1993). Investments of uncertain cost. J. Financial Econom. 34, 53–76.Google Scholar
Revuz, D. and Yor, M. (1991). Continuous Martingales and Brownian Motion. Springer, Berlin.Google Scholar
Schröder, M. (2003). Brownian excursions and Parisian barrier options: a note. J. Appl. Prob. 40, 855–864.Google Scholar
Tseng, C.-L. and Barz, G. (2002). Short-term generation asset valuation: a real options approach. Operat. Res. 50, 297–310.Google Scholar