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Optimal time to invest when the price processes are geometric Brownian motions

Author

Listed:
  • Yaozhong Hu

    () (Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045, USA)

  • Bernt Øksendal

    () (Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway and Institute of Finance and Management Science, Norwegian School of Economics and Business Administration, Helleveien 30, N-5035 Bergen-Sandviken, Norway Manuscript)

Abstract

Let $X_1(t)$, $\cdots$, $X_n(t)$ be $n$ geometric Brownian motions, possibly correlated. We study the optimal stopping problem: Find a stopping time $\tau^*

Suggested Citation

  • Yaozhong Hu & Bernt Øksendal, 1998. "Optimal time to invest when the price processes are geometric Brownian motions," Finance and Stochastics, Springer, vol. 2(3), pages 295-310.
  • Handle: RePEc:spr:finsto:v:2:y:1998:i:3:p:295-310
    Note: received: April 1996; final version received: July 1997
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    Cited by:

    1. Masaya Okawa & Motoh Tsujimura, 2009. "The value of a merger and its optimal timing," Applied Financial Economics, Taylor & Francis Journals, vol. 19(18), pages 1477-1485.
    2. Louberge, Henri & Villeneuve, Stephane & Chesney, Marc, 2002. "Long-term risk management of nuclear waste: a real options approach," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 157-180, November.
    3. Makasu, Cloud, 2010. "A note on explicit bounds for a stopped Feynman-Kac functional," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1977-1979, December.
    4. Luis H. R. Alvarez & Erkki Koskela, 2002. "Irreversible Investment under Interest Rate Variability: New Results," CESifo Working Paper Series 640, CESifo Group Munich.
    5. repec:spr:joptap:v::y::i::d:10.1007_s10957-017-1065-8 is not listed on IDEAS
    6. Rohlfs, Wilko & Madlener, Reinhard, 2010. "Valuation of CCS-Ready Coal-Fired Power Plants: A Multi-Dimensional Real Options Approach," FCN Working Papers 7/2010, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    7. Makasu, Cloud, 2008. "On mean exit time from a curvilinear domain," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2859-2863, December.
    8. Luis H.R. Alvarez & Jukka Lempa & Elias Oikarinen, 2009. "Do Standard Real Option Models Overestimate the Required Rate of Return of Real Estate Investment Opportunities?," Discussion Papers 52, Aboa Centre for Economics.
    9. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
    10. Arkin Vadim & Arkina Svetlana & Slastnikov Alexander, 2003. "Investment Stimulation by a Depreciation Mechanism," EERC Working Paper Series 02-05e, EERC Research Network, Russia and CIS.
    11. Thijssen, Jacco J.J., 2008. "Optimal and strategic timing of mergers and acquisitions motivated by synergies and risk diversification," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1701-1720, May.
    12. Аркин В.И. & Сластников А.Д., 2014. "Моделирование Механизма Государственных Гарантий И Кредитной Политики Банка При Инвестировании Рискованных Проектов," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 50(3), pages 105-118, июль.
    13. GAHUNGU, Joachim & SMEERS, Yves, 2011. "Sufficient and necessary conditions for perpetual multi-assets exchange options," CORE Discussion Papers 2011035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Chiara D'Alpaos & Marina Bertolini & Michele Moretto, 2016. "Do Smart Grids Boost Investment in Photovoltaics? The Prosumer Investment Decision," "Marco Fanno" Working Papers 0203, Dipartimento di Scienze Economiche "Marco Fanno".
    15. Hong Liu & Jianjun Miao, 2006. "Managerial Preferences, Corporate Governance, and Financial Structure," Boston University - Department of Economics - Working Papers Series WP2006-020, Boston University - Department of Economics.
    16. Luis H. R. Alvarez & Erkki Koskela, 2006. "Irreversible Investment under Interest Rate Variability: Some Generalizations," The Journal of Business, University of Chicago Press, vol. 79(2), pages 623-644, March.
    17. GAHUNGU, Joachim & SMEERS, Yves, 2011. "Optimal time to invest when the price processes are geometric Brownian motions. A tentative based on smooth fit," CORE Discussion Papers 2011034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Hampe, Jona & Madlener, Reinhard, 2012. "Economics of High-Temperature Nuclear Reactors for Industrial Cogeneration," FCN Working Papers 10/2012, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).

    More about this item

    Keywords

    Geometric Brownian motion; optimal stopping time; continuation region; stopping set;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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