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

## Author Info

• 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)

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## 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^*

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## Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 2 (1998)
Issue (Month): 3 ()
Pages: 295-310

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Handle: RePEc:spr:finsto:v:2:y:1998:i:3:p:295-310

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## Related research

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

Find related papers by JEL classification:

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

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## Citations

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Cited by:
1. 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).
2. Luis H.R. Alvarez & Erkki Koskela, 2004. "Irreversible investment under interest rate variability: new results," Others 0404007, EconWPA.
3. Jean-Paul Decamps & Thomas Mariotti & Stephane Villeneuve, 2003. "Investment Timing under Incomplete Information," STICERD - Theoretical Economics Paper Series 444, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
4. 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).
5. 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.
6. 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.
7. 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).
8. 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.
9. Makasu, Cloud, 2008. "On mean exit time from a curvilinear domain," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2859-2863, December.
10. 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.
11. 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.

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