Analisis Cadangan Premi Joint Life Insurance Berdasarkan Hukum De Moivre dan Makeham dengan Metode Commissioners dan Fackler Menggunakan Archimedean Copula

Faizah, Afniyah (2025) Analisis Cadangan Premi Joint Life Insurance Berdasarkan Hukum De Moivre dan Makeham dengan Metode Commissioners dan Fackler Menggunakan Archimedean Copula. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Asuransi jiwa joint life merupakan asuransi yang menanggung risiko kematian beberapa orang dengan uang pertanggungan diberikan setelah kematian pertama dari tertanggung. Dalam asuransi joint life, hubungan antar tertanggung dapat dimodelkan dengan Copula. Dalam keluarga Archimedean Copula, terdapat berbagai anggota dengan karakteristik tail dependence yang berbeda. Untuk menjamin kemampuan membayar klaim, perusahaan asuransi harus menghitung cadangan premi. Metode perhitungan cadangan premi seperti metode Commissioners dan Fackler telah dikembangkan untuk menyesuaikan kebutuhan perusahaan asuransi. Cadangan premi bergantung pada penggunaan tabel mortalitas, yang merefleksikan karakteristik risiko kematian berdasarkan usia dan faktor lain, seperti hukum De Moivre dan hukum Makeham. Penelitian ini bertujuan untuk membandingkan perhitungan cadangan premi menggunakan hukum De Moivre dan hukum Makeham dengan metode Commissioners dan Fackler. Selain itu, pendekatan Archimedean Copula digunakan untuk memodelkan ketergantungan pasangan tertanggung dalam asuransi joint life. Suku bunga yang digunakan mengikuti BI-Rate yang berlaku, yakni 6%. Hukum De Moivre menghasilkan probabilitas kematian linear yang kurang realistis dibandingkan hukum Makeham, yang lebih halus dan konsisten dengan Tabel Mortalitas Indonesia IV, ditunjukkan dengan residual standar error hukum Makeham yang lebih rendah dari hukum De Moivre. Variasi usia masuk pasangan, Kendall’s tau, serta jenis Copula memiliki pengaruh terhadap nilai actuarial present value, anuitas, dan premi asuransi. Usia pasangan yang lebih tua menyebabkan meningkatnya premi asuransi, sedangkan Kendall’s tau lebih tinggi menyebabkan turunnya premi asuransi, kecuali pada Frank Copula dengan hukum Makeham yang tidak terdapat perbedaan signifikan. Metode cadangan premi prospektif Commissioners dan retrospektif Fackler menunjukkan pola serupa, dengan cadangan tertinggi pada penggunaan Fackler dengan Frank Copula, Kendall’s tau 0,5, dan hukum De Moivre, sedangkan cadangan terendah ditemukan pada penggunaan Commissioners dengan Clayton Copula, Kendall’s tau 0,75, dan hukum Makeham.
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Joint life insurance is an insurance that covers the risk of death for multiple life, with the benefit paid upon the first death among the insured. In joint life insurance, the relationship between the insured can be modeled using Copula. Within the Archimedean Copula family, there are various members with different tail dependence characteristics. To ensure the ability to pay claims, insurance companies must calculate premium reserves. Methods for calculating premium reserves, such as the Commissioners and Fackler methods, have been developed to meet the needs of insurance companies. Premium reserves depend on the use of mortality tables, which reflect the characteristics of mortality risk based on age and other factors, such as De Moivre's law and Makeham's law. This study aims to compare premium reserve calculations using De Moivre's law and Makeham's law with the Commissioners and Fackler methods. Additionally, the Archimedean Copula approach is employed to model the dependence between insured pairs in joint life insurance. The interest rate used follows the prevailing BI-Rate, which is 6%. De Moivre's law produces a linear probability of death that is less realistic compared to Makeham's law, which is smoother and more consistent with the Indonesian Mortality Table IV, as indicated by a lower residual standard error for Makeham's law. Variations in the entry age of pairs, Kendall’s tau, and the type of Copula affect the actuarial present value, annuities, and insurance premiums. Older entry ages for pairs result in higher insurance premiums, while higher Kendall’s tau leads to lower premiums, except for the Frank Copula with Makeham’s law, where no significant differences are observed. The prospective Commissioners method and the retrospective Fackler method exhibit similar patterns, with the highest reserves found using the Fackler method with the Frank Copula, Kendall’s tau of 0.5, and De Moivre's law, while the lowest reserves are observed using the Commissioners method with the Clayton Copula, Kendall’s tau of 0.75, and Makeham's law.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Asuransi Jiwa, Archimedean Copula, Cadangan Premi, Hukum Mortalitas, Joint Life, Life Insurance, Mortality Law, Premium Reserves.
Subjects:	H Social Sciences > HG Finance > HG8051 Insurance H Social Sciences > HG Finance > HG8054.5 Risk (Insurance) H Social Sciences > HG Finance > HG8771 Life insurance Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Architecture, Design, and Planning > Visual Communication Design > 90241-(S1) Undergraduate Thesis
Depositing User:	Afniyah Faizah
Date Deposited:	08 Jan 2025 03:36
Last Modified:	08 Jan 2025 03:36
URI:	http://repository.its.ac.id/id/eprint/116223

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