IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v304y2023i3p1052-1062.html
   My bibliography  Save this article

Investments with declining cost following a Lévy process

Author

Listed:
  • Armerin, Fredrik

Abstract

We consider an optimal investment problem in which the cost of the investment decreases over time. This decrease is modelled using the negative of a non-decreasing Lévy process. The decreasing cost is a way of modelling that innovations drive down the cost of the investment. We present general results on how to compute both the value of the investment, as well as the optimal time at which the investment should be done. Several explicit examples of how different Lévy processes influence the value of the investment are given as illustrations of the general results. The main tools used are fluctuation theory for Lévy processes and inversion of Laplace transforms. When the inversion can be done analytically, we can present analytical solutions where in some cases only numerical solution has previously been known.

Suggested Citation

  • Armerin, Fredrik, 2023. "Investments with declining cost following a Lévy process," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1052-1062.
    • Handle: RePEc:eee:ejores:v:304:y:2023:i:3:p:1052-1062
    DOI: 10.1016/j.ejor.2022.05.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722003599
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.05.001?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. 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. Farzin, Y. H. & Huisman, K. J. M. & Kort, P. M., 1998. "Optimal timing of technology adoption," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 779-799, May.
    3. Christian Flor & Simon Hansen, 2013. "Technological advances and the decision to invest," Annals of Finance, Springer, vol. 9(3), pages 383-420, August.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Hagspiel, Verena & Nunes, Cláudia & Oliveira, Carlos & Portela, Manuel, 2021. "Green investment under time-dependent subsidy retraction risk," Journal of Economic Dynamics and Control, Elsevier, vol. 126(C).
    9. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    10. Aase, Knut K., 2005. "The perpetual American put option for jump-diffusions with applications," Discussion Papers 2005/12, Norwegian School of Economics, Department of Business and Management Science.
    11. 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.
    12. 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).
    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. 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. 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.
    3. Armerin, Fredrik, 2020. "Investments with declining cost following a Lévy process," Working Paper Series 20/14, Royal Institute of Technology, Department of Real Estate and Construction Management & Banking and Finance.
    4. 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.
    5. Mariotti, Thomas & Décamps, Jean-Paul & Gensbittel, Fabien, 2021. "Investment Timing and Technological Breakthrough," CEPR Discussion Papers 16246, C.E.P.R. Discussion Papers.
    6. 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.
    7. Hagspiel, V. & Huisman, Kuno & Kort, Peter M. & Nunes, Claudia & Pimentel, Rita, 2018. "Product Innovation of an Incumbent Firm : A Dynamic Analysis," Discussion Paper 2018-048, Tilburg University, Center for Economic Research.
    8. Ferrari, Giorgio & Salminen, Paavo, 2016. "Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary," Center for Mathematical Economics Working Papers 530, Center for Mathematical Economics, Bielefeld University.
    9. Christian Flor & Simon Hansen, 2013. "Technological advances and the decision to invest," Annals of Finance, Springer, vol. 9(3), pages 383-420, August.
    10. Demirci, Ece Zeliha & Erkip, Nesim, 2024. "Integrating efforts for product development and market penetration," European Journal of Operational Research, Elsevier, vol. 312(3), pages 927-937.
    11. Peter Kort & Maria Lavrutich & Cláudia Nunes & Carlos Oliveira, 2022. "Preventing Environmental Disasters in Investment under Uncertainty," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 83(1), pages 199-220, September.
    12. Giorgio Ferrari & Paavo Salminen, 2014. "Irreversible Investment under L\'evy Uncertainty: an Equation for the Optimal Boundary," Papers 1411.2395, arXiv.org.
    13. Davis, Graham A. & Cairns, Robert D., 2012. "Good timing: The economics of optimal stopping," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 255-265.
    14. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1422-1460, October.
    15. José Azevedo‐Pereira & Gualter Couto & Cláudia Nunes, 2010. "Optimal timing of relocation," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 6(2), pages 143-163, April.
    16. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    17. 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.
    18. Carol Alexander & Xi Chen, 2021. "Model risk in real option valuation," Annals of Operations Research, Springer, vol. 299(1), pages 1025-1056, April.
    19. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.
    20. Hwa-Sung Kim, 2023. "Effects of ambiguity on innovation strategies," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-27, December.

    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:304:y:2023:i:3:p:1052-1062. 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.