Optimality of a barrier strategy in a spectrally negative Lévy model with a level-dependent intensity of bankruptcy
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909321943580672 |
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| author | Mata, Dante Renaud, Jean-François |
| author_facet | Mata, Dante Renaud, Jean-François |
| contents | We consider de Finetti's stochastic control problem for a spectrally negative Lévy process in an Omega model. In such a model, the (controlled) process is allowed to spend time under the critical level but is then subject to a level-dependent intensity of bankruptcy. First, before considering the control problem, we derive some analytical properties of the corresponding Omega scale functions. Second, we prove that exists a barrier strategy that is optimal for this control problem under a mild assumption on the Lévy measure. Finally, we analyse numerically the impact of the bankruptcy rate function on the optimal strategy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_13849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimality of a barrier strategy in a spectrally negative Lévy model with a level-dependent intensity of bankruptcy Mata, Dante Renaud, Jean-François Probability Optimization and Control 60G51, 93E20, 45D05 We consider de Finetti's stochastic control problem for a spectrally negative Lévy process in an Omega model. In such a model, the (controlled) process is allowed to spend time under the critical level but is then subject to a level-dependent intensity of bankruptcy. First, before considering the control problem, we derive some analytical properties of the corresponding Omega scale functions. Second, we prove that exists a barrier strategy that is optimal for this control problem under a mild assumption on the Lévy measure. Finally, we analyse numerically the impact of the bankruptcy rate function on the optimal strategy. |
| title | Optimality of a barrier strategy in a spectrally negative Lévy model with a level-dependent intensity of bankruptcy |
| topic | Probability Optimization and Control 60G51, 93E20, 45D05 |
| url | https://arxiv.org/abs/2409.13849 |