IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1509.04135.html
   My bibliography  Save this paper

Analytical solution to an investment problem under uncertainties with shocks

Author

Listed:
  • Cl'audia Nunes
  • Rita Pimentel

Abstract

We derive the optimal investment decision in a project where both demand and investment costs are stochastic processes, eventually subject to shocks. We extend the approach used in Dixit and Pindyck (1994), chapter 6.5, to deal with two sources of uncertainty, but assuming that the underlying processes are no longer geometric Brownian diffusions but rather jump diffusion processes. For the class of isoelastic functions that we address in this paper, it is still possible to derive a closed expression for the value of the firm. We prove formally that the result we get is indeed the solution of the optimization problem.

Suggested Citation

  • Cl'audia Nunes & Rita Pimentel, 2015. "Analytical solution to an investment problem under uncertainties with shocks," Papers 1509.04135, arXiv.org, revised Sep 2015.
    • Handle: RePEc:arx:papers:1509.04135
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1509.04135
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    3. Wu, Liang-Chuan & Li, Shu-Hsing & Ong, Chorng-Shyong & Pan, Chungteh, 2012. "Options in technology investment games: The real world TFT-LCD industry case," Technological Forecasting and Social Change, Elsevier, vol. 79(7), pages 1241-1253.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    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. Yanyun Liu & Baiqing Sun, 2023. "Investment strategies of duopoly firms with asymmetric time-to-build under a jump-diffusion model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(3), pages 377-410, December.
    2. 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.
    3. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    4. 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.
    5. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
    6. Ye, Fanglin & Paulson, Nicholas & Khanna, Madhu, 2024. "Strategic innovation and technology adoption under technological uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 165(C).
    7. 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.
    8. 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).
    9. Zeng, Bingxin & Zhu, Lei & Yao, Xing, 2020. "Policy choice for end-of-pipe abatement technology adoption under technological uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 121-130.
    10. S H Martzoukos, 2009. "Real R&D options and optimal activation of two-dimensional random controls," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(6), pages 843-858, June.
    11. Pringles, Rolando & Olsina, Fernando & Garcés, Francisco, 2014. "Designing regulatory frameworks for merchant transmission investments by real options analysis," Energy Policy, Elsevier, vol. 67(C), pages 272-280.
    12. Lauren Chenarides & Mark Manfredo & Timothy J. Richards, 2021. "COVID‐19 and Food Supply Chains," Applied Economic Perspectives and Policy, John Wiley & Sons, vol. 43(1), pages 270-279, March.
    13. Ketelaars, Martijn W. & Kort, Peter M., 2025. "On subsidization of investments in R&D and production capacity," European Journal of Operational Research, Elsevier, vol. 321(3), pages 1036-1054.
    14. Gordon Briest & Elmar Lukas & Sascha H. Mölls & Timo Willershausen, 2020. "Innovation speed under uncertainty and competition," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(8), pages 1517-1527, December.
    15. Driouchi, Tarik & Leseure, Michel & Bennett, David, 2009. "A robustness framework for monitoring real options under uncertainty," Omega, Elsevier, vol. 37(3), pages 698-710, June.
    16. Lukas, Elmar & Reuer, Jeffrey J. & Welling, Andreas, 2012. "Earnouts in mergers and acquisitions: A game-theoretic option pricing approach," European Journal of Operational Research, Elsevier, vol. 223(1), pages 256-263.
    17. Pereira, Paulo J. & Rodrigues, Artur, 2014. "Investment decisions in finite-lived monopolies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 219-236.
    18. Khansa, Lara & Liginlal, Divakaran, 2009. "Valuing the flexibility of investing in security process innovations," European Journal of Operational Research, Elsevier, vol. 192(1), pages 216-235, January.
    19. Driouchi, Tarik & Bennett, David & Simpson, Gary, 2010. "A path-dependent contingent-claims approach to capacity investments," European Journal of Operational Research, Elsevier, vol. 201(1), pages 319-323, February.
    20. Arasteh, Abdollah, 2017. "Considering the investment decisions with real options games approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 72(C), pages 1282-1294.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1509.04135. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.