IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v259y2017i3p1054-1063.html
   My bibliography  Save this article

Analytical solution for an investment problem under uncertainties with shocks

Author

Listed:
  • Nunes, Cláudia
  • Pimentel, Rita

Abstract

We derive the optimal investment decision in a project where both demand and investment cost are stochastic processes, eventually subject to shocks. We extend the approach used in Dixit and Pindyck (1994) to deal with two sources of uncertainty and we assume that the underlying processes are jump diffusion processes. Assuming certain conditions on the parameters, we are able to derive a closed expression for the value of the firm. Finally, we present comparative statics for the investment threshold with respect to the relevant parameters.

Suggested Citation

  • Nunes, Cláudia & Pimentel, Rita, 2017. "Analytical solution for an investment problem under uncertainties with shocks," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1054-1063.
    • Handle: RePEc:eee:ejores:v:259:y:2017:i:3:p:1054-1063
    DOI: 10.1016/j.ejor.2017.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717300139
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.01.008?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. Bar-Ilan, Avner & Sulem, Agnes & Zanello, Alessandro, 2002. "Time-to-build and capacity choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 69-98, January.
    2. Wenbo Shi, 2016. "Entry and exit of service providers under cost uncertainty: a real options approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(2), pages 229-239, February.
    3. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    4. Majd, Saman & Pindyck, Robert S., 1987. "Time to build, option value, and investment decisions," Journal of Financial Economics, Elsevier, vol. 18(1), pages 7-27, March.
    5. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    6. Alghalith, Moawia, 2016. "A note on the theory of the firm under multiple uncertainties," European Journal of Operational Research, Elsevier, vol. 251(1), pages 341-343.
    7. Martzoukos, Spiros H. & Trigeorgis, Lenos, 2002. "Real (investment) options with multiple sources of rare events," European Journal of Operational Research, Elsevier, vol. 136(3), pages 696-706, February.
    8. 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.
    9. Pennings, Enrico & Sereno, Luigi, 2011. "Evaluating pharmaceutical R&D under technical and economic uncertainty," European Journal of Operational Research, Elsevier, vol. 212(2), pages 374-385, July.
    10. Kenneth J. Arrow & Anthony C. Fisher, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 4, pages 76-84, Palgrave Macmillan.
    11. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    12. Oh, Sechan & Rhodes, James & Strong, Ray, 2016. "Impact of cost uncertainty on pricing decisions under risk aversion," European Journal of Operational Research, Elsevier, vol. 253(1), pages 144-153.
    13. Hagspiel, Verena & Huisman, Kuno J.M. & Nunes, Clàudia, 2015. "Optimal technology adoption when the arrival rate of new technologies changes," European Journal of Operational Research, Elsevier, vol. 243(3), pages 897-911.
    14. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    15. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    16. Milne, Alistair & Whalley, A Elizabeth, 2000. "'Time to build, option value and investment decisions': a comment," Journal of Financial Economics, Elsevier, vol. 56(2), pages 325-332, May.
    17. Murto, Pauli, 2007. "Timing of investment under technological and revenue-related uncertainties," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1473-1497, May.
    18. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    19. Pedro Miguel Pimentel & Jos� Azevedo-Pereira & Gualter Couto, 2012. "High-speed rail transport valuation," The European Journal of Finance, Taylor & Francis Journals, vol. 18(2), pages 167-183, February.
    20. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    21. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    22. Zambujal-Oliveira, João & Duque, João, 2011. "Operational asset replacement strategy: A real options approach," European Journal of Operational Research, Elsevier, vol. 210(2), pages 318-325, April.
    23. Gualter Couto & Cláudia Nunes & Pedro Pimentel, 2015. "High-speed rail transport valuation and conjecture shocks," The European Journal of Finance, Taylor & Francis Journals, vol. 21(10-11), pages 791-805, August.
    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. Hagspiel, Verena & Huisman, Kuno J.M. & Kort, Peter M. & Lavrutich, Maria N. & Nunes, Cláudia & Pimentel, Rita, 2020. "Technology adoption in a declining market," European Journal of Operational Research, Elsevier, vol. 285(1), pages 380-392.
    2. Tine Compernolle & Kuno J. M. Huisman & Peter M. Kort & Maria Lavrutich & Cláudia Nunes & Jacco J. J. Thijssen, 2021. "Investment Decisions with Two-Factor Uncertainty," JRFM, MDPI, vol. 14(11), pages 1-17, November.
    3. Thijssen, Jacco J.J., 2022. "Optimal investment and abandonment decisions for projects with construction uncertainty," European Journal of Operational Research, Elsevier, vol. 298(1), pages 368-379.
    4. Barbosa, Luciana & Nunes, Cláudia & Rodrigues, Artur & Sardinha, Alberto, 2020. "Feed-in tariff contract schemes and regulatory uncertainty," European Journal of Operational Research, Elsevier, vol. 287(1), pages 331-347.
    5. Armerin, Fredrik, 2023. "Investments with declining cost following a Lévy process," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1052-1062.
    6. Nunes, Cláudia & Oliveira, Carlos & Pimentel, Rita, 2021. "Quasi-analytical solution of an investment problem with decreasing investment cost due to technological innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 130(C).
    7. Carol Alexander & Xi Chen, 2021. "Model risk in real option valuation," Annals of Operations Research, Springer, vol. 299(1), pages 1025-1056, April.
    8. Støre, Kristian & Fleten, Stein-Erik & Hagspiel, Verena & Nunes, Cláudia, 2018. "Switching from oil to gas production in a depleting field," European Journal of Operational Research, Elsevier, vol. 271(2), pages 710-719.

    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. Nunes, Cláudia & Oliveira, Carlos & Pimentel, Rita, 2021. "Quasi-analytical solution of an investment problem with decreasing investment cost due to technological innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 130(C).
    2. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2006. "Irreversible investment in alternative projects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 425-448, June.
    3. Rena Sivitanidou, 1999. "Does the Theory of Irreversible Investments Help Explain Movements in Office-Commerical Construction?," Working Paper 8659, USC Lusk Center for Real Estate.
    4. Nagae, Takeshi & Akamatsu, Takashi, 2008. "A generalized complementarity approach to solving real option problems," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1754-1779, June.
    5. Delaney, L., 2020. "A Model of Investment under Uncertainty with Time to Build, Market Incompleteness and Risk Aversion," Working Papers 20/13, Department of Economics, City University London.
    6. Delaney, Laura, 2021. "A model of investment under uncertainty with time to build, market incompleteness and risk aversion," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1155-1167.
    7. Akamatsu, Takashi & Nagae, Takeshi, 2011. "A network of options: Evaluating complex interdependent decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 714-729, May.
    8. El-Shazly Alaa, 2004. "Investment Under Uncertainty in Egypt: A Real-Options Approach," Review of Middle East Economics and Finance, De Gruyter, vol. 2(2), pages 51-60, August.
    9. Lukas, Elmar & Mölls, Sascha & Welling, Andreas, 2016. "Venture capital, staged financing and optimal funding policies under uncertainty," European Journal of Operational Research, Elsevier, vol. 250(1), pages 305-313.
    10. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    11. Walsh, D.M. & O'Sullivan, K. & Lee, W.T. & Devine, M.T., 2014. "When to invest in carbon capture and storage technology: A mathematical model," Energy Economics, Elsevier, vol. 42(C), pages 219-225.
    12. Fredrik Armerin & Han-Suck Song, 2021. "A framework for modelling cash flow lags," SN Business & Economics, Springer, vol. 1(10), pages 1-13, October.
    13. 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.
    14. Spiros H. Martzoukos & Nayia Pospori & Lenos Trigeorgis, 2024. "Corporate investment decisions with switch flexibility, constraints, and path-dependency," Review of Quantitative Finance and Accounting, Springer, vol. 62(3), pages 1223-1250, April.
    15. Saphores, Jean-Daniel & Gravel, Éric & Bernard, Jean-Thomas, 2003. "Environmental Impact Assessment and Investment under Uncertainty. An Application to Power Grid Interconnection," Cahiers de recherche 0303, GREEN.
    16. Masci, Martín Ezequiel, 2012. "Irreversibilidad e incertidumbre de las decisiones financieras en i&d [Irreversibility and uncertainty of the financial investments on r&d]," MPRA Paper 40970, University Library of Munich, Germany.
    17. Steven R. Grenadier, 2003. "An Equilibrium Analysis of Real Estate," NBER Working Papers 9475, National Bureau of Economic Research, Inc.
    18. Thijssen, Jacco J.J., 2015. "A model for irreversible investment with construction and revenue uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 250-266.
    19. Grenadier, Steven R. & Wang, Neng, 2005. "Investment timing, agency, and information," Journal of Financial Economics, Elsevier, vol. 75(3), pages 493-533, March.
    20. Pindyck, Robert S, 1991. "Irreversibility, Uncertainty, and Investment," Journal of Economic Literature, American Economic Association, vol. 29(3), pages 1110-1148, September.

    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:eee:ejores:v:259:y:2017:i:3:p:1054-1063. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.