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Stopping of functionals with discontinuity at the boundary of an open set

Author

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  • Palczewski, Jan
  • Stettner, Lukasz

Abstract

We explore properties of the value function and existence of optimal stopping times for functionals with discontinuities related to the boundary of an open (possibly unbounded) set . The stopping horizon is either random, equal to the first exit from the set , or fixed (finite or infinite). The payoff function is continuous with a possible jump at the boundary of . Using a generalization of the penalty method, we derive a numerical algorithm for approximation of the value function for general Feller-Markov processes and show existence of optimal or [epsilon]-optimal stopping times.

Suggested Citation

  • Palczewski, Jan & Stettner, Lukasz, 2011. "Stopping of functionals with discontinuity at the boundary of an open set," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2361-2392, October.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:10:p:2361-2392
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    References listed on IDEAS

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    1. Lamberton, Damien, 2009. "Optimal stopping with irregular reward functions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3253-3284, October.
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    Cited by:

    1. Tiziano De Angelis, 2020. "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon," Papers 2009.01276, arXiv.org, revised Jan 2022.
    2. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2020. "Optimal hedging of a perpetual American put with a single trade," Papers 2003.06249, arXiv.org, revised Sep 2020.

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