Optimal stopping of the stable process with state-dependent killing
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910347020992512 |
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| author | van Schaik, K. Watson, A. R. Xu, X. |
| author_facet | van Schaik, K. Watson, A. R. Xu, X. |
| contents | We describe the solution of an optimal stopping problem for a stable Lévy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains self-similar, and the solution to the optimal stopping problem is obtained by characterising a self-similar Markov process associated with the stable process. The optimal stopping strategy is to stop upon first passage into an interval, found explicitly in terms of the parameters of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03610 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal stopping of the stable process with state-dependent killing van Schaik, K. Watson, A. R. Xu, X. Probability 60G40, 60G51 We describe the solution of an optimal stopping problem for a stable Lévy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains self-similar, and the solution to the optimal stopping problem is obtained by characterising a self-similar Markov process associated with the stable process. The optimal stopping strategy is to stop upon first passage into an interval, found explicitly in terms of the parameters of the model. |
| title | Optimal stopping of the stable process with state-dependent killing |
| topic | Probability 60G40, 60G51 |
| url | https://arxiv.org/abs/2207.03610 |