A characterization of ruin-inducing probability measures in a renewal risk model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914509770194944 |
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| author | Tzaninis, Spyridon M. Bozikas, Apostolos |
| author_facet | Tzaninis, Spyridon M. Bozikas, Apostolos |
| contents | In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(γ,δ)$. This result allows us to obtain an explicit representation of the infinite-time ruin probability as an expectation under any ruin-inducing probability measure. A key feature of our approach is that the construction of these measures does not rely on the existence of moment generating functions, and is therefore applicable to heavy-tailed claim size distributions. The proposed framework includes the classical Esscher transform as a special case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A characterization of ruin-inducing probability measures in a renewal risk model Tzaninis, Spyridon M. Bozikas, Apostolos Probability Primary 91G05, secondary 60G44, 60K05 In this work, we derive a complete characterization of all ruin-inducing probability measures that preserve the structure of a given compound renewal process in terms of suitable pairs of functions $(γ,δ)$. This result allows us to obtain an explicit representation of the infinite-time ruin probability as an expectation under any ruin-inducing probability measure. A key feature of our approach is that the construction of these measures does not rely on the existence of moment generating functions, and is therefore applicable to heavy-tailed claim size distributions. The proposed framework includes the classical Esscher transform as a special case. |
| title | A characterization of ruin-inducing probability measures in a renewal risk model |
| topic | Probability Primary 91G05, secondary 60G44, 60K05 |
| url | https://arxiv.org/abs/2604.24061 |