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A Verification Theorem for Optimal Stopping Problems with Expectation Constraints

A Verification Theorem for Optimal Stopping Problems with Expectation Constraints 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Verification Theorem for Optimal Stopping Problems with Expectation Constraints

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References (13)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-017-9424-2
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 10, 2017

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