Modified ruin probability for a Cramér-Lundberg model driven by a compound mixed Poisson process
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915991221436416 |
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| author | Sakuma, Noriyoshi Tashiro, Momoka |
| author_facet | Sakuma, Noriyoshi Tashiro, Momoka |
| contents | We study modified ruin probabilities in a Cramér-Lundberg model driven by a compound mixed Poisson process. In the heavy-tailed regime, if the integrated claim-size distribution is subexponential and the upper endpoint of the mixing distribution stays below the net-profit boundary, the modified and classical ruin probabilities are asymptotically equivalent. In the light-tailed regime, we prove a fixed-intensity ratio theorem and obtain both an endpoint-atom result and a sharp endpoint-density asymptotic with an explicit constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modified ruin probability for a Cramér-Lundberg model driven by a compound mixed Poisson process Sakuma, Noriyoshi Tashiro, Momoka Probability 91G05 We study modified ruin probabilities in a Cramér-Lundberg model driven by a compound mixed Poisson process. In the heavy-tailed regime, if the integrated claim-size distribution is subexponential and the upper endpoint of the mixing distribution stays below the net-profit boundary, the modified and classical ruin probabilities are asymptotically equivalent. In the light-tailed regime, we prove a fixed-intensity ratio theorem and obtain both an endpoint-atom result and a sharp endpoint-density asymptotic with an explicit constant. |
| title | Modified ruin probability for a Cramér-Lundberg model driven by a compound mixed Poisson process |
| topic | Probability 91G05 |
| url | https://arxiv.org/abs/2605.07059 |