IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v91y2020i3d10.1007_s00186-019-00694-6.html
   My bibliography  Save this article

Some results on optimal stopping under phase-type distributed implementation delay

Author

Listed:
  • Jukka Lempa

    (University of Turku)

Abstract

We study optimal stopping of strong Markov processes under random implementation delay. By random implementation delay we mean the following: the payoff is not realised immediately when the process is stopped but rather after a random waiting period. The distribution of the random waiting period is assumed to be phase-type. We prove first a general result on the solvability of the problem. Then we study the case of Coxian distribution both in general and with scalar diffusion dynamics in more detail. The study is concluded with two explicit examples.

Suggested Citation

  • Jukka Lempa, 2020. "Some results on optimal stopping under phase-type distributed implementation delay," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 559-583, June.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:3:d:10.1007_s00186-019-00694-6
    DOI: 10.1007/s00186-019-00694-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-019-00694-6
    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/s00186-019-00694-6?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. Alvarez, Luis H. R. & Keppo, Jussi, 2002. "The impact of delivery lags on irreversible investment under uncertainty," European Journal of Operational Research, Elsevier, vol. 136(1), pages 173-180, January.
    2. 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.
    3. Avner Bar-Ilan & Agnès Sulem, 1995. "Explicit Solution of Inventory Problems with Delivery Lags," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 709-720, August.
    4. Alvarez, Luis H. R. & Stenbacka, Rune, 2001. "Adoption of uncertain multi-stage technology projects: a real options approach," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 71-97, February.
    5. 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.
    6. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
    7. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    8. Mark Fackrell, 2009. "Modelling healthcare systems with phase-type distributions," Health Care Management Science, Springer, vol. 12(1), pages 11-26, March.
    9. James L. Paddock & Daniel R. Siegel & James L. Smith, 1988. "Option Valuation of Claims on Real Assets: The Case of Offshore Petroleum Leases," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(3), pages 479-508.
    10. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    11. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    12. Aïd, René & Federico, Salvatore & Pham, Huyên & Villeneuve, Bertrand, 2015. "Explicit investment rules with time-to-build and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 240-256.
    13. 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.
    14. Titman, Sheridan, 1985. "Urban Land Prices under Uncertainty," American Economic Review, American Economic Association, vol. 75(3), pages 505-514, June.
    15. Williams, Joseph T, 1993. "Equilibrium and Options on Real Assets," Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 825-850.
    16. Capozza, Dennis & Li, Yuming, 1994. "The Intensity and Timing of Investment: The Case of Land," American Economic Review, American Economic Association, vol. 84(4), pages 889-904, September.
    17. Sarkar, Sudipto & Zhang, Chuanqian, 2015. "Investment policy with time-to-build," Journal of Banking & Finance, Elsevier, vol. 55(C), pages 142-156.
    18. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    19. Bar-Ilan, Avner & Strange, William C, 1996. "Investment Lags," American Economic Review, American Economic Association, vol. 86(3), pages 610-622, June.
    20. Worawat Margsiri & Antonio S. Mello & Martin E. Ruckes, 2008. "A Dynamic Analysis of Growth via Acquisition," Review of Finance, European Finance Association, vol. 12(4), pages 635-671.
    21. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
    22. Jukka Lempa, 2012. "Optimal stopping with random exercise lag," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 273-286, June.
    23. 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.
    24. Panayi, Sylvia & Trigeorgis, Lenos, 1998. "Multi-stage Real Options: The Cases of Information Technology Infrastructure and International Bank Expansion," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(3, Part 2), pages 675-692.
    25. Grenadier, Steven R, 1996. "The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets," Journal of Finance, American Finance Association, vol. 51(5), pages 1653-1679, December.
    26. Bladt, Mogens, 2005. "A Review on Phase-type Distributions and their Use in Risk Theory," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 145-161, May.
    27. repec:dau:papers:123456789/14292 is not listed on IDEAS
    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. Armerin, Fredrik & Song, Han-Suck, 2020. "A framework for modelling cash flow lags," Working Paper Series 20/17, Royal Institute of Technology, Department of Real Estate and Construction Management & Banking and Finance.
    2. Fredrik Armerin & Han-Suck Song, 2021. "A framework for modelling cash flow lags," SN Business & Economics, Springer, vol. 1(10), pages 1-13, October.

    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. Lander, Diane M. & Pinches, George E., 1998. "Challenges to the Practical Implementation of Modeling and Valuing Real Options," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(3, Part 2), pages 537-567.
    2. 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.
    3. Bulan, Laarni & Mayer, Christopher & Somerville, C. Tsuriel, 2009. "Irreversible investment, real options, and competition: Evidence from real estate development," Journal of Urban Economics, Elsevier, vol. 65(3), pages 237-251, May.
    4. Carlos Andrés Zapata Quimbayo, 2020. "OPCIONES REALES Una guía teórico-práctica para la valoración de inversiones bajo incertidumbre mediante modelos en tiempo discreto y simulación de Monte Carlo," Books, Universidad Externado de Colombia, Facultad de Finanzas, Gobierno y Relaciones Internacionales, number 138, April.
    5. Bolton, Patrick & Wang, Neng & Yang, Jinqiang, 2019. "Investment under uncertainty with financial constraints," Journal of Economic Theory, Elsevier, vol. 184(C).
    6. Rose Neng Lai & Lawrence Hoc Nang Fong, 2021. "Development Strategies in a Market of High Vacancies and Sticky Rates – The Case of the Hotel Industry," International Real Estate Review, Global Social Science Institute, vol. 24(3), pages 363-383.
    7. Laarni T. Bulan, 2005. "Real options, irreversible investment and firm uncertainty: New evidence from U.S. firms," Review of Financial Economics, John Wiley & Sons, vol. 14(3-4), pages 255-279.
    8. Steven R. Grenadier, 2003. "An Equilibrium Analysis of Real Estate," NBER Working Papers 9475, National Bureau of Economic Research, Inc.
    9. Gkochari, Christiana C., 2015. "Optimal investment timing in the dry bulk shipping sector," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 102-109.
    10. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    11. Bulan, Laarni T., 2005. "Real options, irreversible investment and firm uncertainty: New evidence from U.S. firms," Review of Financial Economics, Elsevier, vol. 14(3-4), pages 255-279.
    12. Clapp, John M. & Bardos, Katsiaryna Salavei & Wong, S.K., 2012. "Empirical estimation of the option premium for residential redevelopment," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 240-256.
    13. Lambrecht, Bart M., 2017. "Real options in finance," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 166-171.
    14. Luis M. Abadie & José M. Chamorro, 2009. "Monte Carlo valuation of natural gas investments," Review of Financial Economics, John Wiley & Sons, vol. 18(1), pages 10-22, January.
    15. Fredrik Armerin & Han-Suck Song, 2021. "A framework for modelling cash flow lags," SN Business & Economics, Springer, vol. 1(10), pages 1-13, October.
    16. 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.
    17. Chi-Yo Huang & Hong-Ling Hsieh & Hueiling Chen, 2020. "Evaluating the Investment Projects of Spinal Medical Device Firms Using the Real Option and DANP-mV Based MCDM Methods," IJERPH, MDPI, vol. 17(9), pages 1-41, May.
    18. Andrianos Tsekrekos & George Kanoutos, 2013. "Real Options Premia Implied from Recent Transactions in the Greek Real Estate Market," The Journal of Real Estate Finance and Economics, Springer, vol. 47(1), pages 152-168, July.
    19. Collan, Mikael, 2004. "Giga-Investments: Modelling the Valuation of Very Large Industrial Real Investments," MPRA Paper 4328, University Library of Munich, Germany.
    20. Kim, Ki Hong & Hwang, Seong Tae & Oh, Hyung Sik & Lee, Deok Joo, 2008. "The impact of investment lags on investment decision," European Journal of Operational Research, Elsevier, vol. 190(3), pages 696-707, November.

    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:mathme:v:91:y:2020:i:3:d:10.1007_s00186-019-00694-6. 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.