On the time consistent solution to optimal stopping problems with expectation constraint
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911914778427392 |
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| author | Christensen, Sören Klein, Maike Schultz, Boy |
| author_facet | Christensen, Sören Klein, Maike Schultz, Boy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05378 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the time consistent solution to optimal stopping problems with expectation constraint Christensen, Sören Klein, Maike Schultz, Boy Probability Optimization and Control 60G40, 60J70, 91A25, 91B51 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. |
| title | On the time consistent solution to optimal stopping problems with expectation constraint |
| topic | Probability Optimization and Control 60G40, 60J70, 91A25, 91B51 |
| url | https://arxiv.org/abs/2311.05378 |