Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula
One of the multi-life annuity products is a reversionary annuity, a life annuity product for two insured people. The annuity payment for this product will begin after one of the insured specified in the contract dies first until the other insured dies as well. The calculation of the annuity premium...
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| Format: | Article |
| Language: | English |
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Department of Mathematics, Universitas Negeri Gorontalo
2022-06-01
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| Series: | Jambura Journal of Mathematics |
| Subjects: | |
| Online Access: | https://ejurnal.ung.ac.id/index.php/jjom/article/view/13952 |
| _version_ | 1818116813408436224 |
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| author | Furlo Gilbert Godfrey I Gusti Putu Purnaba Ruhiyat Ruhiyat |
| author_facet | Furlo Gilbert Godfrey I Gusti Putu Purnaba Ruhiyat Ruhiyat |
| author_sort | Furlo Gilbert Godfrey |
| collection | DOAJ |
| description | One of the multi-life annuity products is a reversionary annuity, a life annuity product for two insured people. The annuity payment for this product will begin after one of the insured specified in the contract dies first until the other insured dies as well. The calculation of the annuity premium is usually done by assuming independence between the random variable of remaining life-times of the insured parties. However, this is not relevant to the actual situation because the husband and wife are interrelated with their lives. This study considered this relationship when modelling the joint distribution of the remaining life-times between husband and wife. Frank’s copula was used to model the joint distribution of the remaining life-times of husband and wife. It was built from marginal distribution, which was assumed to follow the mortality value in the 2019 Indonesian Mortality Table IV. The mortality value at non-integer ages was assumed to follow a uniform distribution (uniform distribution of death). Furthermore, the joint survival distribution modelled by copula was constructed exactly when husband and wife are married. This study also considered the net single premium of reversionary annuity for several beneficiary cases. In general, the results of the calculation of the net single premium with Frank’s copula produced a lower value than the calculation of the assumption of independence for all beneficiary cases. In addition, the purchase time of an annuity also affects the net single premium, which increases up to a certain point of marriage age and then decreases thereafter. |
| first_indexed | 2024-12-11T04:28:29Z |
| format | Article |
| id | doaj.art-d75ced86893d4fd38625c67692bcaf6e |
| institution | Directory Open Access Journal |
| issn | 2654-5616 2656-1344 |
| language | English |
| last_indexed | 2024-12-11T04:28:29Z |
| publishDate | 2022-06-01 |
| publisher | Department of Mathematics, Universitas Negeri Gorontalo |
| record_format | Article |
| series | Jambura Journal of Mathematics |
| spelling | doaj.art-d75ced86893d4fd38625c67692bcaf6e2022-12-22T01:20:55ZengDepartment of Mathematics, Universitas Negeri GorontaloJambura Journal of Mathematics2654-56162656-13442022-06-014210.34312/jjom.v4i2.139524196Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s CopulaFurlo Gilbert Godfrey0I Gusti Putu Purnaba1Ruhiyat Ruhiyat2IPB UniversityIPB UniversityIPB UniversityOne of the multi-life annuity products is a reversionary annuity, a life annuity product for two insured people. The annuity payment for this product will begin after one of the insured specified in the contract dies first until the other insured dies as well. The calculation of the annuity premium is usually done by assuming independence between the random variable of remaining life-times of the insured parties. However, this is not relevant to the actual situation because the husband and wife are interrelated with their lives. This study considered this relationship when modelling the joint distribution of the remaining life-times between husband and wife. Frank’s copula was used to model the joint distribution of the remaining life-times of husband and wife. It was built from marginal distribution, which was assumed to follow the mortality value in the 2019 Indonesian Mortality Table IV. The mortality value at non-integer ages was assumed to follow a uniform distribution (uniform distribution of death). Furthermore, the joint survival distribution modelled by copula was constructed exactly when husband and wife are married. This study also considered the net single premium of reversionary annuity for several beneficiary cases. In general, the results of the calculation of the net single premium with Frank’s copula produced a lower value than the calculation of the assumption of independence for all beneficiary cases. In addition, the purchase time of an annuity also affects the net single premium, which increases up to a certain point of marriage age and then decreases thereafter.https://ejurnal.ung.ac.id/index.php/jjom/article/view/13952frank’s copulamarried couplenet single premiumreversionary annuityuniform distribution of death |
| spellingShingle | Furlo Gilbert Godfrey I Gusti Putu Purnaba Ruhiyat Ruhiyat Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula Jambura Journal of Mathematics frank’s copula married couple net single premium reversionary annuity uniform distribution of death |
| title | Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula |
| title_full | Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula |
| title_fullStr | Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula |
| title_full_unstemmed | Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula |
| title_short | Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula |
| title_sort | penentuan premi tunggal bersih pada reversionary annuity untuk pasangan suami istri dengan model frank s copula |
| topic | frank’s copula married couple net single premium reversionary annuity uniform distribution of death |
| url | https://ejurnal.ung.ac.id/index.php/jjom/article/view/13952 |
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