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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.18164 |
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| _version_ | 1866911969248804864 |
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| author | Locas, Félix Renaud, Jean-François |
| author_facet | Locas, Félix Renaud, Jean-François |
| contents | We consider de Finetti's optimal dividends problem with absolutely continuous strategies in a spectrally negative Lévy model with Parisian ruin as the termination time. The problem considered is essentially a generalization of both the control problems considered by Kyprianou, Loeffen & Pérez (2012) and by Renaud (2019). Using the language of scale functions for Parisian fluctuation theory, and under the assumption that the density of the Lévy measure is completely monotone, we prove that a refraction dividend strategy is optimal and we characterize the optimal threshold. In particular, we study the effect of the rate of Parisian implementation delays on this optimal threshold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18164 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimality of a refraction strategy in the optimal dividends problem with absolutely continuous controls subject to Parisian ruin Locas, Félix Renaud, Jean-François Probability Optimization and Control We consider de Finetti's optimal dividends problem with absolutely continuous strategies in a spectrally negative Lévy model with Parisian ruin as the termination time. The problem considered is essentially a generalization of both the control problems considered by Kyprianou, Loeffen & Pérez (2012) and by Renaud (2019). Using the language of scale functions for Parisian fluctuation theory, and under the assumption that the density of the Lévy measure is completely monotone, we prove that a refraction dividend strategy is optimal and we characterize the optimal threshold. In particular, we study the effect of the rate of Parisian implementation delays on this optimal threshold. |
| title | Optimality of a refraction strategy in the optimal dividends problem with absolutely continuous controls subject to Parisian ruin |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2310.18164 |