IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i1d10.1007_s00362-019-01088-w.html
   My bibliography  Save this article

The optimal stopping problem revisited

Author

Listed:
  • Manuel Guerra

    (Universidade de Lisboa)

  • Cláudia Nunes

    (Universidade de Lisboa)

  • Carlos Oliveira

    (Universidade de Lisboa
    Universidade de Lisboa)

Abstract

We consider an optimal stopping time problem, related with many models found in real options problems. We present analytical solutions for a broad class of gain functions, considering quite general assumptions over the model. Also, an extensive and general sensitivity analysis is provided.

Suggested Citation

  • Manuel Guerra & Cláudia Nunes & Carlos Oliveira, 2021. "The optimal stopping problem revisited," Statistical Papers, Springer, vol. 62(1), pages 137-169, February.
  • Handle: RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-019-01088-w
    DOI: 10.1007/s00362-019-01088-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-019-01088-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00362-019-01088-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Huisman, K.J.M. & Kort, P.M., 1999. "Strategic Technology Investment under Uncertainty," Discussion Paper 1999-18, Tilburg University, Center for Economic Research.
    2. Hagspiel, Verena & Huisman, Kuno J.M. & Kort, Peter M. & Nunes, Cláudia, 2016. "How to escape a declining market: Capacity investment or Exit?," European Journal of Operational Research, Elsevier, vol. 254(1), pages 40-50.
    3. René Carmona & Savas Dayanik, 2008. "Optimal Multiple Stopping of Linear Diffusions," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 446-460, May.
    4. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    5. Stéphane Villeneuve & Jean-Paul Descamps, 2007. "Optimal Dividend Policy and Growth Option," Post-Print hal-00173171, HAL.
    6. Alvarez, Luis H. R., 1999. "Optimal exit and valuation under demand uncertainty: A real options approach," European Journal of Operational Research, Elsevier, vol. 114(2), pages 320-329, April.
    7. Savas Dayanik, 2008. "Optimal Stopping of Linear Diffusions with Random Discounting," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 645-661, August.
    8. Michail Chronopoulos & Verena Hagspiel & Stein-Erik Fleten, 2017. "Stepwise investment and capacity sizing under uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 447-472, March.
    9. Jean-Paul Décamps & Stéphane Villeneuve, 2007. "Optimal dividend policy and growth option," Finance and Stochastics, Springer, vol. 11(1), pages 3-27, January.
    10. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    11. Stéphane Villeneuve, 2007. "On the Threshold Strategies and Smooth-Fit Principle For Optimal Stopping Problems," Post-Print hal-00173165, HAL.
    12. Nancy Stokey, 2016. "Wait-and See: Investment Options under Policy Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 21, pages 246-265, July.
    13. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    14. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-349, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    2. Nader Karimi & Erfan Salavati & Hirbod Assa & Hojatollah Adibi, 2023. "Sensitivity Analysis of Optimal Commodity Decision Making with Neural Networks: A Case for COVID-19," Mathematics, MDPI, vol. 11(5), pages 1-15, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bolton, Patrick & Wang, Neng & Yang, Jinqiang, 2019. "Investment under uncertainty with financial constraints," Journal of Economic Theory, Elsevier, vol. 184(C).
    2. Adkins, Roger & Paxson, Dean, 2019. "Rescaling-contraction with a lower cost technology when revenue declines," European Journal of Operational Research, Elsevier, vol. 277(2), pages 574-586.
    3. de Angelis, Tiziano & Ferrari, Giorgio & Martyr, Randall & Moriarty, John, 2016. "Optimal entry to an irreversible investment plan with non convex costs," Center for Mathematical Economics Working Papers 566, Center for Mathematical Economics, Bielefeld University.
    4. Pauli Murto & Marko Terviö, 2014. "Exit Options And Dividend Policy Under Liquidity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(1), pages 197-221, February.
    5. Alvarez, Luis H. R., 1998. "Exit strategies and price uncertainty: a Greenian approach," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 43-56, January.
    6. Tsekrekos, Andrianos E., 2010. "The effect of mean reversion on entry and exit decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 725-742, April.
    7. Tauer, Loren W., 2006. "When to Get In and Out of Dairy Farming: A Real Option Analysis," Agricultural and Resource Economics Review, Cambridge University Press, vol. 35(2), pages 339-347, October.
    8. Li, Lingfei & Linetsky, Vadim, 2014. "Optimal stopping in infinite horizon: An eigenfunction expansion approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 122-128.
    9. Qiang Li & Junwei Wang & Jian Ni & Lap Keung Chu & Congdong Li, 2019. "The optimal time to make a risky investment under a permanent exit option," Journal of Intelligent Manufacturing, Springer, vol. 30(7), pages 2669-2680, October.
    10. Aïd, René & Li, Liangchen & Ludkovski, Michael, 2017. "Capacity expansion games with application to competition in power generation investments," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 1-31.
    11. Jyh-Bang Jou, 2000. "Irreversible Investment Decisions Under Uncertainty with Tax Holidays," Public Finance Review, , vol. 28(1), pages 66-81, January.
    12. Lu, Jin-Ray & Hwang, Chih-Chiang & Lin, Chien-Yi, 2016. "Do shareholders appreciate capital investment policies of corporations?," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 344-353.
    13. Cui, Chuantao & Li, Leona Shao-Zhi, 2023. "Trade policy uncertainty and new firm entry: Evidence from China," Journal of Development Economics, Elsevier, vol. 163(C).
    14. Shackleton, Mark B. & Tsekrekos, Andrianos E. & Wojakowski, Rafal, 2004. "Strategic entry and market leadership in a two-player real options game," Journal of Banking & Finance, Elsevier, vol. 28(1), pages 179-201, January.
    15. Andrianos Tsekrekos, 2013. "Irreversible exit decisions under mean-reverting uncertainty," Journal of Economics, Springer, vol. 110(1), pages 5-23, September.
    16. H. Dharma Kwon, 2010. "Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream," Operations Research, INFORMS, vol. 58(3), pages 638-649, June.
    17. Delong Li & Mr. Nicolas E Magud & Mr. Fabian Valencia, 2015. "Corporate Investment in Emerging Markets: Financing vs. Real Options Channel," IMF Working Papers 2015/285, International Monetary Fund.
    18. Egami, Masahiko, 2009. "A framework for the study of expansion options, loan commitments and agency costs," Journal of Corporate Finance, Elsevier, vol. 15(3), pages 345-357, June.
    19. Avner Bar-Ilan & Yishay D. Maoz, 2021. "Choosing a Price and Cost Combination—The Role of Correlation," JRFM, MDPI, vol. 14(11), pages 1-13, November.
    20. Isik, Murat & Coble, Keith H. & Hudson, Darren & House, Lisa O., 2003. "A model of entry-exit decisions and capacity choice under demand uncertainty," Agricultural Economics, Blackwell, vol. 28(3), pages 215-224, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-019-01088-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.