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Applied Mathematics & Optimization

, Volume 79, Issue 1, pp 145–177 | Cite as

A Verification Theorem for Optimal Stopping Problems with Expectation Constraints

  • Stefan AnkirchnerEmail author
  • Maike Klein
  • Thomas Kruse
Article

Abstract

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.

Keywords

Optimal stopping Expectation constraints Dynamic programming principle Verification theorem 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Institute for MathematicsUniversity of JenaJenaGermany
  2. 2.Faculty of MathematicsUniversity of Duisburg-EssenEssenGermany

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