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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.10538 |
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| _version_ | 1866911463483899904 |
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| author | Egami, Masahiko Koike, Tomohiro |
| author_facet | Egami, Masahiko Koike, Tomohiro |
| contents | We establish a systematic solution method for optimal stopping problems of spectrally negative Lévy processes. Our approach relies essentially on the potential theory, in particular the Riesz decomposition and the maximum principle. Using these mathematical results, we not only derive necessary and sufficient conditions of optimality for a broad class of reward functions, but also develop a method to tackle general problems in a direct and constructive way (without pre-specifying the solution form). To reinforce the latter point, we provide a step-by-step solution procedure applicable to complex solution structures, including continuation regions with multiple connected components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A potential-theoretic approach to optimal stopping in a spectrally Lévy Model Egami, Masahiko Koike, Tomohiro Optimization and Control Probability Primary 60G40, Secondary 60J76 We establish a systematic solution method for optimal stopping problems of spectrally negative Lévy processes. Our approach relies essentially on the potential theory, in particular the Riesz decomposition and the maximum principle. Using these mathematical results, we not only derive necessary and sufficient conditions of optimality for a broad class of reward functions, but also develop a method to tackle general problems in a direct and constructive way (without pre-specifying the solution form). To reinforce the latter point, we provide a step-by-step solution procedure applicable to complex solution structures, including continuation regions with multiple connected components. |
| title | A potential-theoretic approach to optimal stopping in a spectrally Lévy Model |
| topic | Optimization and Control Probability Primary 60G40, Secondary 60J76 |
| url | https://arxiv.org/abs/2506.10538 |