Lévy processes under level-dependent Poissonian switching
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910041897959424 |
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| author | Beelders, Noah Ramsden, Lewis Papaioannou, Apostolos D. |
| author_facet | Beelders, Noah Ramsden, Lewis Papaioannou, Apostolos D. |
| contents | In this paper, we derive identities for the upward and downward exit problems and resolvents for a process whose motion changes between two Lévy processes if it is above (or below) a barrier $b$ and coincides with a Poissonian arrival time. This can be expressed in the form of a (hybrid) stochastic differential equation, for which the existence of its solution is also discussed. All identities are given in terms of new generalisations of scale functions (counterparts of the scale functions from the theory of Lévy processes). To illustrate the applicability of our results, the probability of ruin is obtained for a risk process with delays in the dividend payments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lévy processes under level-dependent Poissonian switching Beelders, Noah Ramsden, Lewis Papaioannou, Apostolos D. Probability 60G51 In this paper, we derive identities for the upward and downward exit problems and resolvents for a process whose motion changes between two Lévy processes if it is above (or below) a barrier $b$ and coincides with a Poissonian arrival time. This can be expressed in the form of a (hybrid) stochastic differential equation, for which the existence of its solution is also discussed. All identities are given in terms of new generalisations of scale functions (counterparts of the scale functions from the theory of Lévy processes). To illustrate the applicability of our results, the probability of ruin is obtained for a risk process with delays in the dividend payments. |
| title | Lévy processes under level-dependent Poissonian switching |
| topic | Probability 60G51 |
| url | https://arxiv.org/abs/2505.00453 |