On the Time Consistent Solution to Optimal Stopping Problems with Expectation Constraint

We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of randomized but purely state dependent stopping times as admissibl...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 91; no. 1; p. 11
Main Authors Christensen, S., Klein, M., Schultz, B.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2025
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Constraints
Control
Equilibrium
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Simulation
Systems Theory
Theoretical
Time dependence
Time consistent solution
Expectation constraint
Optimal stopping
60G40
60J70
91A25
91B51
Equilibrium
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Summary:We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of randomized but purely state dependent stopping times as admissible strategies. We derive a verification theorem and necessary conditions for equilibria, which together basically characterize all equilibria. Furthermore, additional structural properties of equilibria are obtained to feed a possible guess-and-verify approach, which is then illustrated by an example.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10202-w