Zaidan, Muhammad Rafli Alta (2025) Penerapan Strict Archimedean Copula untuk Model Dependensi Sisa Waktu Hidup pada Produk Reversionary Annuity dengan Mortalitas Gompertz-Makeham Diperumum. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Penelitian ini mengeksplorasi perhitungan premi tunggal dan berjangka bersih untuk produk reversionary annuity dengan pendekatan inovatif menggunakan dependensi strict Archimedean copula dan hukum mortalitas Gompertz-Makeham (r,s) diperumum. Fokus utama penelitian adalah mempersiapkan kebutuhan perlindungan finansial bagi anak-anak dalam situasi single parenting, di mana reversionary annuity menyediakan pendapatan tetap setelah kematian salah satu orang tua. Model dependensi sisa hidup bersama dengan berbagai jenis copula, seperti Clayton, Gumbel-Hougaard, NSA 12, dan NSA 14, diintegrasikan dengan hukum mortalitas GM, yang menawarkan fleksibilitas tinggi dalam memodelkan tabel mortalitas karena keberadaan dua jenis parameter yang memungkinkan penyesuaian terhadap pola mortalitas yang kompleks. Hasil penelitian menunjukkan bahwa copula Gumbel-Hougaard memberikan nilai premi tertinggi, sedangkan Clayton cocok untuk skenario dengan ketergantungan lebih rendah. Pada contoh kasus, pasangan suami istri berusia 40 tahun dapat memilih pembayaran premi tunggal sebesar Rp89,19 juta atau premi berjangka Rp10,08 juta pertahun maksimal selama 10 tahun untuk memperoleh manfaat tahunan reversionary annuity sebesar Rp50 juta selama pasangan yang ditinggalkan masih hidup. Penelitian ini memberikan kontribusi penting bagi pengembangan model aktuaria di Indonesia, khususnya dalam desain produk reversionary annuity, dengan menawarkan panduan yang lebih efektif untuk perhitungan premi dan perencanaan pensiun berbasis ketergantungan sisa waktu hidup bersama.
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This study explores the calculation of single and term net premiums for reversionary annuity products using an innovative approach that incorporates strict Archimedean copula dependency and the generalized Gompertz-Makeham (r,s) mortality law. The primary focus is to address the financial protection needs of children in single-parenting situations, where reversionary annuities provide steady income after the death of one parent. The dependency model for joint lifetimes is constructed using various copulas, including Clayton, GumbelHougaard, NSA 12, and NSA 14, integrated with the GM mortality law, which offers high flexibility in modeling mortality tables through two parameters that allow adaptation to complex mortality patterns. The results indicate that the Gumbel-Hougaard copula yields the highest premium values, while the Clayton copula is more suitable for scenarios with lower dependency levels. For instance, a married couple aged 40 years can opt for a single premium payment of IDR 89.19 million or a term premium of IDR 10.08 million per year for a maximum of 10 years to receive an annual reversionary annuity benefit of IDR 50 million as long as the surviving spouse remains alive. This research provides significant contributions to the development of actuarial models in Indonesia, particularly in designing reversionary annuity products, by offering more effective guidelines for premium calculation and retirement planning based on joint lifetime dependency.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Copula, Gompertz-Makeham, Reversionary Annuity, Premi Tunggal, Premi Berjangka, Periodic Premium, Single Premium |
| Subjects: | Q Science > QA Mathematics > QA401 Mathematical models. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis |
| Depositing User: | Muhammad Rafli Alta Zaidan |
| Date Deposited: | 13 Jan 2025 06:22 |
| Last Modified: | 13 Jan 2025 06:22 |
| URI: | http://repository.its.ac.id/id/eprint/116251 |
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