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arXiv · 1006.4283

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

Jan Palczewski·Lukasz Stettner
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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 $\mathcal{O}$. The stopping horizon is either random, equal to the first exit from the set $\mathcal{O}$, or fixed: finite or infinite. The payoff function is continuous with a possible jump at the boundary of $\mathcal{O}$. 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 $ε$-optimal stopping times.

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Jan Palczewski, Lukasz Stettner. 2011-04-28. Stopping of functionals with discontinuity at the boundary of an open set. https://doi.org/10.1016/j.spa.2011.05.013

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