Asymptotics of Ruin Probabilities in a Subordinated Cramér-Lundberg Model
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914363252670464 |
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| author | Klinge, Jonathan Schmeck, Maren Diane |
| author_facet | Klinge, Jonathan Schmeck, Maren Diane |
| contents | We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events, this process is time-changed by a Lévy subordinator. The subordinator is chosen so that it evolves, on average, at the same speed as calendar time, creating a trade-off between intensity and severity. We show that such a transformation always has a negative impact on the probability of ruin. Despite the expected total claim amount remaining invariant, it turns out that the probability of ruin as a function of the initial capital falls arbitrarily slowly depending on the choice of the subordinator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01821 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics of Ruin Probabilities in a Subordinated Cramér-Lundberg Model Klinge, Jonathan Schmeck, Maren Diane Risk Management Probability 62P05, 91B05, 91G05 We study a dynamic model of a non-life insurance portfolio. The foundation of the model is a compound Poisson process that represents the claims side of the insurer. To introduce clusters of claims appearing, e.g. with catastrophic events, this process is time-changed by a Lévy subordinator. The subordinator is chosen so that it evolves, on average, at the same speed as calendar time, creating a trade-off between intensity and severity. We show that such a transformation always has a negative impact on the probability of ruin. Despite the expected total claim amount remaining invariant, it turns out that the probability of ruin as a function of the initial capital falls arbitrarily slowly depending on the choice of the subordinator. |
| title | Asymptotics of Ruin Probabilities in a Subordinated Cramér-Lundberg Model |
| topic | Risk Management Probability 62P05, 91B05, 91G05 |
| url | https://arxiv.org/abs/2603.01821 |