Zaki, R. Dastin Albany (2025) Analisis Perhitungan Premi Reversionary Annuity Model Dynamic Bivariate Common Shock Dengan Hukum Gamma-Gompertz Dan Weibull Dengan Suku Bunga Stokastik. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Industri asuransi jiwa memiliki peran penting dalam perlindungan finansial, terutama dalam skema joint life insurance. Salah satu produknya adalah reversionary annuity, yang memberikan pembayaran kepada penerima manfaat setelah kematian tertanggung utama. Model Dynamic Bivariate Common Shock (DBCS) digunakan untuk menangkap ketergantungan antarindividu akibat kejadian common shock bersama yang bersifat kumulatif, seperti kecelakaan fatal atau bencana alam. Penelitian ini mengembangkan metode perhitungan premi reversionary annuity dengan mempertimbangkan hukum mortalitas Gamma-Gompertz dan Weibull serta suku bunga stokastik model Cox-Ingersoll-Ross (CIR). Fungsi intensitas kejadian common shock dimodelkan dengan Nonhomogeneous Poisson Process (NHPP) dirumuskan sebagai fungsi naik. Perhitungan hasil premi dilakukan pada premi tunggal dan berjangka dengan dua variasi usia pasangan (tahun), di antaranya pasangan 1: suami berusia 46 dan istri berusia 45; pasangan 2: suami berusia 56 dan istri berusia 55. Proyeksi suku bunga diperoleh melalui simulasi Monte Carlo sebanyak 10000 kali dengan nilai MAPE sebesar 17,3%. Parameter Gamma-Gompertz menghasilkan RSE sebesar 4,2% untuk laki-laki dan 4,3% untuk perempuan. Di sisi lain, model Weibull menunjukkan tingkat adjusted R-squared sebesar 96%. Hasil analisis menunjukkan bahwa nilai premi untuk pendekatan DBCS tidak jauh berbeda dengan pendekatan independen, yang disebabkan oleh fungsi intensitas shock yang sangat kecil. Hal ini mengindikasikan bahwa probabilitas kejadian kematian simultan akibat common shock sangat rendah sehingga penyintas tetap memiliki harapan hidup panjang. Selain itu, model Weibull tetap menunjukkan kecenderungan menghasilkan premi lebih tinggi karena sensitivitasnya terhadap umur panjang. Dengan demikian, pemilihan model mortalitas dan bentuk fungsi intensitas shock menjadi faktor krusial dalam menentukan nilai premi yang adil dan berkelanjutan. Penelitian ini diharapkan dapat membantu industri asuransi dalam merancang strategi penetapan premi yang lebih akurat dan adaptif terhadap risiko kematian akibat common shock di Indonesia.
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The life insurance industry plays a vital role in financial protection, particularly through joint life insurance schemes. One of its products is the reversionary annuity, which provides payments to the beneficiary after the death of the primary insured. The Dynamic Bivariate Common Shock (DBCS) model is used to capture the dependency between individuals caused by cummulative common shock events, such as fatal accidents or natural disasters. This study develops a method for calculating reversionary annuity premiums by considering the Gamma-Gompertz and Weibull laws, as well as the stochastic interest rate modeled using Cox-Ingersoll-Ross (CIR) framework. The shock intensity function is modeled using a Nonhomogeneous Poisson Process (NHPP) and defined as increasing function. Premium calculations are carried out for single and term premiums using two age scenarios: couple 1 (husband aged 46, wife aged 45) and couple 2 (husband aged 56, wife aged 55). The interest rate is projected via 10000 Monte Carlo simulations, resulting in a MAPE of 17,3%. The Gamma-Gompertz model yields RSE values of 4.2% for males and 4.3% for females, while the Weibull model shows a strong performance with an adjusted R-squared of 96%. The analysis reveals that the premium values under the DBCS approach are not significantly different from the independent approach due to the very low shock intensity function, indicating that the probability of simultaneous death from a common shock is minimal, allowing the survivor to maintain a long-life expectancy. Furthermore, the Weibull model consistently produces higher premium values due to its sensitivity to longevity. Thus, selecting an appropriate mortality model and intensity function is crucial for determining fair and sustainable premium values. This research is expected to assist the insurance industry in designing more accurate and adaptive premium strategies for mortality risks arising from common shocks in Indonesia.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Reversionary Annuity, Dynamic Bivariate Common Shock, Gamma-Gompertz, Weibull, CIR, Nonhomogeneous Poisson Process |
| Subjects: | Q Science > QA Mathematics > QA184 Algebra, Linear Q Science > QA Mathematics > QA273.6 Weibull distribution. Logistic distribution. Q Science > QA Mathematics > QA274.2 Stochastic analysis Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis |
| Depositing User: | R Dastin Albany Zaki |
| Date Deposited: | 30 Jul 2025 08:17 |
| Last Modified: | 30 Jul 2025 08:17 |
| URI: | http://repository.its.ac.id/id/eprint/123722 |
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