A Verification Theorem for Optimal Stopping Problems with Expectation Constraints
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We consider the problem of optimally stopping a continuous-time process with a stopping time satisfying a given expectation cost constraint. We show, by introducing a new state variable, that one can transform the problem into an unconstrained control problem and hence obtain a dynamic programming principle. We characterize the value function in terms of the dynamic programming equation, which turns out to be an elliptic, fully non-linear partial differential equation of second order. We prove a classical verification theorem and illustrate its applicability with several examples.
KeywordsOptimal stopping Expectation constraints Dynamic programming principle Verification theorem
We are grateful to Bruno Bouchard, Goran Peskir, Mikhail Urusov, Song Yao and Mihail Zervos for helpful comments. We thank an anonymous referee for the careful reading of the manuscript and highly appreciate her/his comments which contributed to improve our paper.
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