On stochastic control under Poisson observations: optimality of a barrier strategy in a general Lévy model
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929593874644992 |
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| author | Noba, Kei Yamazaki, Kazutoshi |
| author_facet | Noba, Kei Yamazaki, Kazutoshi |
| contents | We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general Lévy process, we show the optimality of a periodic barrier strategy, which moves the process upward to the barrier whenever it is observed to be below it. The convergence of the optimal solutions to those in the continuous-observation case is also shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00501 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On stochastic control under Poisson observations: optimality of a barrier strategy in a general Lévy model Noba, Kei Yamazaki, Kazutoshi Optimization and Control Probability We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general Lévy process, we show the optimality of a periodic barrier strategy, which moves the process upward to the barrier whenever it is observed to be below it. The convergence of the optimal solutions to those in the continuous-observation case is also shown. |
| title | On stochastic control under Poisson observations: optimality of a barrier strategy in a general Lévy model |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2210.00501 |