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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.04850 |
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| _version_ | 1866918277979045888 |
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| author | Grigutis, Andrius Lukoševičius, Laurynas Venckevičius, Mindaugas |
| author_facet | Grigutis, Andrius Lukoševičius, Laurynas Venckevičius, Mindaugas |
| contents | In this article, we present several formulas that make it easier to compute the net single premiums when the mortality force over the fractional ages is assumed to be constant (C). More precisely, we compute the moments of the random variables $ν^{T_x}$, $T_x$, $T_xν^{T_x}$, etc., where $T_x$ denotes the future lifetime of a person who is $x\in\{0,\,1,\,\ldots\}$ years old, and $ν$ is the annual discount multiplier. We verify the obtained formulas on the real data from the human mortality table and the Gompertz survival law. The obtained numbers are compared with the corresponding ones when the survival function over fractional ages is interpolated using the uniform distribution of deaths (UDD) and Balducci's (B) assumptions. We also formulate and prove the statement on the comparison of the moments of the mentioned random variables under assumptions (C), (UDD), and (B). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Several expressions of the net single premiums under the constant force of mortality Grigutis, Andrius Lukoševičius, Laurynas Venckevičius, Mindaugas Probability 91G05, 62P05, 62N99 In this article, we present several formulas that make it easier to compute the net single premiums when the mortality force over the fractional ages is assumed to be constant (C). More precisely, we compute the moments of the random variables $ν^{T_x}$, $T_x$, $T_xν^{T_x}$, etc., where $T_x$ denotes the future lifetime of a person who is $x\in\{0,\,1,\,\ldots\}$ years old, and $ν$ is the annual discount multiplier. We verify the obtained formulas on the real data from the human mortality table and the Gompertz survival law. The obtained numbers are compared with the corresponding ones when the survival function over fractional ages is interpolated using the uniform distribution of deaths (UDD) and Balducci's (B) assumptions. We also formulate and prove the statement on the comparison of the moments of the mentioned random variables under assumptions (C), (UDD), and (B). |
| title | Several expressions of the net single premiums under the constant force of mortality |
| topic | Probability 91G05, 62P05, 62N99 |
| url | https://arxiv.org/abs/2601.04850 |