Analisis Perhitungan Premi dan Cadangan Premi untuk Asuransi Berjangka dengan Memperhatikan Mortality Jump

Khofifah, Wafiq (2025) Analisis Perhitungan Premi dan Cadangan Premi untuk Asuransi Berjangka dengan Memperhatikan Mortality Jump. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Perusahaan asuransi jiwa memiliki peran penting dalam menyediakan perlindungan finansial bagi masyarakat. Oleh karena itu, perusahaan asuransi perlu memastikan bahwa perhitungan premi dan cadangan premi mencerminkan secara akurat risiko yang ditanggung. Salah satu risiko signifikan yang perlu diperhatikan adalah peningkatan mendadak dalam tingkat kematian pemegang polis, yang dikenal sebagai mortality jump. Fenomena ini telah terjadi di Indonesia pada beberapa peristiwa besar, seperti tragedi G30S PKI (1965–1966), tsunami Aceh (2004), dan pandemi COVID-19 (2020–2022). Untuk menghadapi tantangan ini, diperlukan metode pemodelan tingkat mortalitas yang mampu menangkap pola lonjakan kematian secara efektif. Dalam penelitian ini, tingkat mortalitas diproyeksikan menggunakan dua pendekatan utama, yaitu model Singular Value Decomposition (SVD) Lee-Carter dan Poisson Log-Bilinear Lee-Carter, kemudian dibandingkan dengan Tabel Mortalitas Indonesia IV (TMI IV). Selain itu, digunakan juga model suku bunga stokastik Cox-Ingersoll-Ross (CIR) untuk menghitung nilai premi dan cadangan premi. Hasil penelitian menunjukkan bahwa baik model SVD Lee-Carter maupun Poisson Log-Bilinear Lee-Carter menghasilkan tingkat mortalitas yang meningkat seiring bertambahnya usia, terutama pada kelompok usia lanjut (70–100 tahun), dan memiliki proyeksi yang relatif serupa satu sama lain. Namun, keduanya menunjukkan perbedaan signifikan dibandingkan dengan TMI IV 2019 pada usia lanjut, mengindikasikan bahwa TMI IV sudah kurang relevan untuk produk asuransi berisiko tinggi. Model CIR menghasilkan rata-rata suku bunga positif sebesar 5,17%. Perhitungan premi dan cadangan premi dengan ketiga tabel mortalitas menunjukkan pola yang serupa, yaitu premi tertinggi diberikan kepada calon tertanggung laki-laki dan berusia tua. Meski hasil antara SVD dan Poisson Log-Bilinear Lee-Carter tidak jauh berbeda, terdapat selisih yang cukup besar jika dibandingkan dengan hasil berbasis TMI IV. Penelitian ini mengungkapkan bahwa model SVD Lee-Carter dan Poisson Log-Bilinear Lee-Carter mampu memproyeksikan tingkat mortalitas secara lebih realistis dibandingkan tabel tradisional. Oleh karena itu, metode ini dapat menjadi dasar pengembangan lebih lanjut dalam pemodelan risiko mortalitas untuk mendukung kestabilan liabilitas dan keberlanjutan industri perasuransian, terutama dalam menghadapi risiko besar seperti mortality jump.
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Life insurance companies play a vital role in providing financial protection to the public. Therefore, it is essential for insurers to ensure that the calculation of premiums and premium reserves accurately reflects the risks undertaken. One significant risk that must be considered is the sudden increase in policyholder mortality, known as a mortality jump. This phenomenon has occurred in Indonesia during major events such as the G30S PKI tragedy (1965–1966), the Aceh tsunami (2004), and the COVID-19 pandemic (2020–2022). To address this challenge, a mortality modeling method capable of capturing mortality jumps effectively is required. In this study, mortality rates were projected using two primary approaches: the Singular Value Decomposition (SVD) Lee-Carter model and the Poisson Log-Bilinear Lee-Carter model, which were then compared to the Indonesian Mortality Table IV (TMI IV). Additionally, the Cox-Ingersoll-Ross (CIR) stochastic interest rate model was applied to calculate life insurance premiums and premium reserves. The results show that both the SVD Lee-Carter and Poisson Log-Bilinear Lee-Carter models produce mortality rates that increase with age, especially for elderly individuals (ages 70–100), and yield relatively similar projections. However, both models exhibit significant differences when compared to TMI IV 2019, particularly in older age groups, suggesting that TMI IV is becoming less relevant for high-risk insurance products. The CIR model yielded a positive average interest rate of 5.17%. Premium and reserve calculations across the three mortality tables show a consistent pattern, with the highest premiums charged to older male policyholders. Although the results from the SVD and Poisson Log-Bilinear Lee-Carter models are closely aligned, there is a considerable difference when compared to the calculations using TMI IV. This research indicates that both the SVD Lee-Carter and Poisson Log-Bilinear Lee-Carter models are capable of projecting mortality more realistically than traditional mortality tables. Therefore, these models can serve as a foundation for further development in mortality risk modeling, supporting the stability of insurance liabilities and the sustainability of the insurance industry, especially in the face of extreme events such as mortality jumps.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Asuransi Jiwa Berjangka, Mortality Jump, Poisson-Log Bilinear Lee-Carter, Singular Value Decomposition (SVD) Lee-Carter, Suku Bunga Cox-Ingersoll-Ross, Term Life Insurance, Mortality Jump, Poisson-Log Bilinear Lee-Carter, Singular Value Decomposition (SVD) Lee-Carter, Interest Rate Cox-Ingersoll-Ross
Subjects:	H Social Sciences > H Social Sciences (General) > H61.4 Forecasting in the social sciences H Social Sciences > HG Finance > HG8051 Insurance H Social Sciences > HG Finance > HG8054.5 Risk (Insurance) H Social Sciences > HG Finance > HG8771 Life insurance
Divisions:	Faculty of Mathematics, Computation, and Data Science > Actuaria > 94203-(S1) Undergraduate Thesis
Depositing User:	Wafiq Khofifah
Date Deposited:	30 Jul 2025 08:05
Last Modified:	30 Jul 2025 08:27
URI:	http://repository.its.ac.id/id/eprint/124229

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