A characterization of equivalent martingale probability measures in a mixed renewal risk model with applications in Risk Theory
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866917738282221568 |
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| author | Tzaninis, Spyridon M. Macheras, Nikolaos D. |
| author_facet | Tzaninis, Spyridon M. Macheras, Nikolaos D. |
| contents | If a given aggregate process $S$ is a compound mixed renewal process under a probability measure $P$, we provide a characterization of all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ is converted into a compound mixed Poisson process under $Q$. This result extends earlier works of Delbaen & Haezendonck [2], Embrechts & Meister [5], Lyberopoulos & Macheras [11], and of the authors [14]. Implications to the ruin problem and to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_09051 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A characterization of equivalent martingale probability measures in a mixed renewal risk model with applications in Risk Theory Tzaninis, Spyridon M. Macheras, Nikolaos D. Probability Primary 91G05, 60C55, Secondary 28A35, 60A10, 60G44, 60K05 If a given aggregate process $S$ is a compound mixed renewal process under a probability measure $P$, we provide a characterization of all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and $S$ is converted into a compound mixed Poisson process under $Q$. This result extends earlier works of Delbaen & Haezendonck [2], Embrechts & Meister [5], Lyberopoulos & Macheras [11], and of the authors [14]. Implications to the ruin problem and to the computation of premium calculation principles in an insurance market possessing the property of no free lunch with vanishing risk are also discussed. |
| title | A characterization of equivalent martingale probability measures in a mixed renewal risk model with applications in Risk Theory |
| topic | Probability Primary 91G05, 60C55, Secondary 28A35, 60A10, 60G44, 60K05 |
| url | https://arxiv.org/abs/2007.09051 |