Optimal Periodic Double-Barrier Strategies for Spectrally Negative Lévy Processes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909626596851712 |
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| author | Yamazaki, Kazutoshi Zhang, Qingyuan |
| author_facet | Yamazaki, Kazutoshi Zhang, Qingyuan |
| contents | We study a stochastic control problem where the underlying process follows a spectrally negative Lévy process. A controller can continuously increase the process but only decrease it at independent Poisson arrival times. We show the optimality of the double-barrier strategy, which increases the process whenever it would fall below some lower barrier and decreases it whenever it is observed above a higher barrier. An optimal strategy and the associated value function are written semi-explicitly using scale functions. Numerical results are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Periodic Double-Barrier Strategies for Spectrally Negative Lévy Processes Yamazaki, Kazutoshi Zhang, Qingyuan Optimization and Control We study a stochastic control problem where the underlying process follows a spectrally negative Lévy process. A controller can continuously increase the process but only decrease it at independent Poisson arrival times. We show the optimality of the double-barrier strategy, which increases the process whenever it would fall below some lower barrier and decreases it whenever it is observed above a higher barrier. An optimal strategy and the associated value function are written semi-explicitly using scale functions. Numerical results are also given. |
| title | Optimal Periodic Double-Barrier Strategies for Spectrally Negative Lévy Processes |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.23080 |