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The Optimal Stopping Problem of Dupuis and Wang: A Generalization

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  • Jukka Lempa

    (Department of Economics, Turku School of Economics)

Abstract

In this paper, we study the optimal stopping problem of Dupuis and Wang analyzed in [7]. In this problem, the underlying follows a linear diffusion but the decision maker is not allowed to stop at any time she desires but rather on the jump times of an independent Poisson process. In [7], the authors solve this problem in the case where the underlying is a geometric Brownian motion and the payoff function is of American call option type. In the current study, we will this problem under weak assumptions on both the underlying and the payoff. We also demonstrate that the results of [7] are recovered from ours.

Suggested Citation

  • Jukka Lempa, 2008. "The Optimal Stopping Problem of Dupuis and Wang: A Generalization," Discussion Papers 36, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp36
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    File URL: http://www.ace-economics.fi/kuvat/dp36.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    More about this item

    Keywords

    Optimal stopping; linear diffusion; free boundary problem; Poisson process;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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