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An investment model with switching costs and the option to abandon

Author

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  • Mihail Zervos

    (London School of Economics)

  • Carlos Oliveira

    (Universidade de Lisboa)

  • Kate Duckworth

    (London School of Economics)

Abstract

We develop a complete analysis of a general entry–exit–scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic indicator such as the price of or the demand for the project’s output commodity. We assume that the investment project can operate in two modes, an “open” one and a “closed” one. The transitions from one operating mode to the other one are costly and immediate, and form a sequence of decisions made by the project’s management. We also assume that the project can be permanently abandoned at a discretionary time and at a constant sunk cost. The objective of the project’s management is to maximise the expected discounted payoff resulting from the project’s management over all switching and abandonment strategies. We derive the explicit solution to this stochastic control problem that involves impulse control as well as discretionary stopping. It turns out that this has a rather rich structure and the optimal strategy can take eight qualitatively different forms, depending on the problems data.

Suggested Citation

  • Mihail Zervos & Carlos Oliveira & Kate Duckworth, 2018. "An investment model with switching costs and the option to abandon," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 417-443, December.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:3:d:10.1007_s00186-018-0641-5
    DOI: 10.1007/s00186-018-0641-5
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    References listed on IDEAS

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    1. Richard R. Lumley & Mihail Zervos, 2001. "A Model for Investments in the Natural Resource Industry with Switching Costs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 637-653, November.
    2. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    3. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    4. Gassiat, Paul & Kharroubi, Idris & Pham, Huyên, 2012. "Time discretization and quantization methods for optimal multiple switching problem," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2019-2052.
    5. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    6. Johnson, Timothy C. & Zervos, Mihail, 2010. "The explicit solution to a sequential switching problem with non-smooth data," LSE Research Online Documents on Economics 29003, London School of Economics and Political Science, LSE Library.
    7. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    8. Aïd, René & Campi, Luciano & Langrené, Nicolas & Pham, Huyên, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," LSE Research Online Documents on Economics 63011, London School of Economics and Political Science, LSE Library.
    9. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    10. Tsekrekos, Andrianos E. & Yannacopoulos, Athanasios N., 2016. "Optimal switching decisions under stochastic volatility with fast mean reversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 148-157.
    11. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
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    13. Erhan Bayraktar & Masahiko Egami, 2010. "On the One-Dimensional Optimal Switching Problem," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 140-159, February.
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