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Optimal stopping with irregular reward functions

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  • Lamberton, Damien

Abstract

We consider optimal stopping problems with finite horizon for one-dimensional diffusions. We assume that the reward function is bounded and Borel-measurable, and we prove that the value function is continuous and can be characterized as the unique solution of a variational inequality in the sense of distributions.

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  • Lamberton, Damien, 2009. "Optimal stopping with irregular reward functions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3253-3284, October.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3253-3284
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    Cited by:

    1. 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.
    2. Jonas Al-Hadad & Zbigniew Palmowski, 2020. "Perpetual American options with asset-dependent discounting," Papers 2007.09419, arXiv.org, revised Jan 2021.
    3. Timothy C. Johnson, 2012. "The solution of discretionary stopping problems with applications to the optimal timing of investment decisions," Papers 1210.2617, arXiv.org.

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