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Optimal stopping with random exercise lag

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  • Jukka Lempa

Abstract

We study optimal stopping with exponentially distributed exercise lag. We formalize the problem first in a general Markovian setting and derive a set of conditions under which the solution exists. In particular, no semicontinuity assumptions of the payoff function are needed. We analyze also some specific classes of lagged optimal stopping problems with one-dimensional diffusion dynamics where the solution can be characterized in closed form. Finally, the results are illustrated with an explicit example. Copyright Springer-Verlag 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:75:y:2012:i:3:p:273-286
    DOI: 10.1007/s00186-012-0384-7
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    References listed on IDEAS

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    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. 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.
    3. Bar-Ilan, Avner & Strange, William C, 1996. "Investment Lags," American Economic Review, American Economic Association, vol. 86(3), pages 610-622, June.
    4. 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.
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    Cited by:

    1. 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.
    2. Guo, Peijun & Li, Yonggang, 2014. "Approaches to multistage one-shot decision making," European Journal of Operational Research, Elsevier, vol. 236(2), pages 612-623.
    3. Gapeev, Pavel V., 2020. "On the problems of sequential statistical inference for Wiener processes with delayed observations," LSE Research Online Documents on Economics 104072, London School of Economics and Political Science, LSE Library.
    4. 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.
    5. Pavel V. Gapeev, 2020. "On the problems of sequential statistical inference for Wiener processes with delayed observations," Statistical Papers, Springer, vol. 61(4), pages 1529-1544, August.
    6. Fredrik Armerin & Han-Suck Song, 2021. "A framework for modelling cash flow lags," SN Business & Economics, Springer, vol. 1(10), pages 1-13, October.

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