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The Effects of Implementation Delay on Decision-Making Under Uncertainty

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  • Erhan Bayraktar
  • Masahiko Egami

Abstract

In this paper, we accomplish two objectives: First, we provide a new mathematical characterization of the value function for impulse control problems with implementation delay and present a direct solution method that differs from its counterparts that use quasi-variational inequalities. Our method is direct, in the sense that we do not have to guess the form of the solution and we do not have to prove that the conjectured solution satisfies conditions of a verification lemma. Second, by employing this direct solution method, we solve two examples that involve decision delays: an exchange rate intervention problem and a problem of labor force optimization.

Suggested Citation

  • Erhan Bayraktar & Masahiko Egami, 2007. "The Effects of Implementation Delay on Decision-Making Under Uncertainty," Papers math/0703833, arXiv.org.
    • Handle: RePEc:arx:papers:math/0703833
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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. Bar-Ilan, Avner & Perry, David & Stadje, Wolfgang, 2004. "A generalized impulse control model of cash management," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1013-1033, March.
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    5. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    6. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
    7. Shepp, Larry & Shiryaev, Albert, 1996. "Hiring and firing optimally in a large corporation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1523-1539.
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    9. Luis Alvarez & Jukka Virtanen, 2006. "A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 373-398, June.
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    Cited by:

    1. Gechun Liang & Zhou Yang, 2018. "Analysis of the optimal exercise boundary of American put options with delivery lags," Papers 1805.02909, arXiv.org, revised Dec 2020.
    2. Katia Colaneri & Tiziano De Angelis, 2019. "A class of recursive optimal stopping problems with applications to stock trading," Papers 1905.02650, arXiv.org, revised Jun 2021.
    3. Erhan Bayraktar & Masahiko Egami, 2008. "An Analysis of Monotone Follower Problems for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 336-350, May.
    4. Erhan Bayraktar & Masahiko Egami, 2010. "A unified treatment of dividend payment problems under fixed cost and implementation delays," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 325-351, April.
    5. 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.
    6. Erhan Bayraktar & Zhou Zhou, 2013. "On an Optimal Stopping Problem of an Insider," Papers 1301.3100, arXiv.org, revised Apr 2015.
    7. 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.
    8. Egami, Masahiko & Young, Virginia R., 2009. "Optimal reinsurance strategy under fixed cost and delay," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 1015-1034, March.
    9. Bruder, Benjamin & Pham, Huyên, 2009. "Impulse control problem on finite horizon with execution delay," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1436-1469, May.

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