Analisis Expected dan Variance Prospective Loss Portofolio Asuransi Jiwa Survivorship (Last-to-Die) denggan Model Suku Bunga Stokastik Cox-Ingersoll-Ross (CIR) dan Copula Mortalitas

Farhana, Khalida Zia (2026) Analisis Expected dan Variance Prospective Loss Portofolio Asuransi Jiwa Survivorship (Last-to-Die) denggan Model Suku Bunga Stokastik Cox-Ingersoll-Ross (CIR) dan Copula Mortalitas. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Asuransi jiwa survivorship (last-to-die) merupakan produk asuransi yang memberikan manfaat pada saat tertanggung terakhir meninggal dunia. Dalam praktik aktuaria, valuasi kewajiban produk tidak hanya memerlukan estimasi nilai kewajiban rata-rata, tetapi juga pengukuran tingkat risiko kewajiban. Penelitian ini betujuan untuk menghitung nilai expected prospective loss dan variance prospective loss pada asuransi jiwa dwiguna survivorship untuk polis tunggal, portofolio homogen, dan portofolio non-homogen dengan mempertimbangkan tingkat suku bunga stokastik dan dependensi mortalitas pasangan suami-istri. Tingkat suku bunga dimodelkan menggunakan Cox-Ingersoll-Ross (CIR) dengan parameter yang diestimasi dari data historis BI 7-Day Reverse Repo Rate periode 2010-2025. Dependen mortalitas dimodelkan menggunakan Archimedean copula, yaitu Clayton copula, Frank copula, dan Gumbel copula, dengan tingkat dependensi yang direpresentasikan oleh Kendall’s Tau sebesar 0,25; 0,50; 0,75. Probabilitas mortalitas diperoleh dari Tabel Mortalitas Mortalitas Indonesia IV. Perhitungan dilakukan dengan bantuan simulasi Monte Carlo sebanyak 1.000 bangkitan. Hasil menunjukkan bahwa tingkat suku bunga hasil proyeksi model CIR berfluktuasi secara stokastik dan cenderung kembali menuju rata-rata jangka panjang sebsar 4,86468%. Ketiga model copula berhasil memodelkan dependensi mortalitas pasangan suami-istri dan menghasilkan peluang kematian bersama yang lebih tinggi dibandingkan asumsi independen. Nilai expected prospective loss meningkat seiring bertambahnya waktu valuasi, sedangkan variance prospective loss cenderung menurun hingga mendekati nol pada akhir masa pertanggungan. Selain itu, asumsi dependen menghasilkan nilai expected prospective loss dan variance prospective loss yang lebih tinggi dibandingkan asumsi independen. Pada portofolio homogen, peningkatan jumlah polis menurunkan risiko melalui efek diversifikasi, sedangkan pada portofolio non-homogen nilai kewajiban dipengaruhi oleh variasi karakteristik polis. Analisis sensitivitas menunjukkan bahwa model CIR lebih sensitif terhadap perubahan paramter long-term mean dibandingkan parameter mean reversion speed.
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Survivorship life insurance (last-to-die) is a life insurance product that provides benefits upon the death of the last surviving insured. In actuarial practice, the valuation of insurance liabilities requires not only the estimation of expected liabilities but also the measurement of liability risk. This study aims to calculate the expected prospective loss and variance of prospective loss for survivorship endowment insurance under single-policy, homogeneous portfolio, and heterogeneous portfolio settings by incorporating stochastic interest rates and mortality dependence between married couples. The interest rate is modeled using the Cox–Ingersoll–Ross (CIR) model, with parameters estimated from historical BI 7-Day Reverse Repo Rate data from 2010 to 2025. Mortality dependence is modeled using Archimedean copulas, namely the Clayton, Frank, and Gumbel copulas, with dependence levels represented by Kendall’s Tau values of 0.25, 0.50, and 0.75. Mortality probabilities are obtained from the Indonesian Mortality Table IV. Calculations are performed using Monte Carlo simulation with 1,000 iterations. The results indicate that interest rates projected by the CIR model fluctuate stochastically and tend to revert to a long-term mean of 4.86468%. All three copula models successfully capture the mortality dependence of married couples and produce higher joint mortality probabilities than the independence assumption. The expected prospective loss increases as the valuation time progresses, whereas the variance of prospective loss generally decreases and approaches zero at the end of the coverage period. Furthermore, dependent mortality assumptions generate higher expected prospective loss and variance values than independent mortality assumptions. In homogeneous portfolios, increasing the number of policies reduces risk through diversification effects, while in heterogeneous portfolios, liability values are influenced by variations in policy characteristics. Sensitivity analysis shows that the CIR model is more sensitive to changes in the long-term mean parameter than to changes in the mean reversion speed parameter.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	CIR, copula, prospective loss, suku bunga stokastik, survivorship. CIR, copula, prospective loss, stochastic interest rate, survivorship.
Subjects:	H Social Sciences > HG Finance > HG8771 Life insurance
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis
Depositing User:	Khalida Zia Farhana
Date Deposited:	20 Jul 2026 01:35
Last Modified:	20 Jul 2026 01:35
URI:	http://repository.its.ac.id/id/eprint/135608

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