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All Journal Mandalika Mathematics and Educations Journal Parameter: Jurnal Matematika, Statistika dan Terapannya
Aldila Nur Indah Berliana Ratam
Institut Teknologi Sumatera
Mathematics

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Pemodelan Premi Asuransi Jiwa Dwiguna Unit Link dengan Metode Annual Ratchet dan Hukum Gompertz Aldila Nur Indah Berliana Ratam; Marisa; Agus Irawan; Nasrullah
Mandalika Mathematics and Educations Journal Vol 8 No 1 (2026): Edisi Maret
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v8i1.11061

Abstract

The risk of death is one of the risks that can have a significant impact on an individual’s financial condition. Therefore, protection through life insurance is required. Unit-linked endowment life insurance combines protection and investment benefits, with the premium amount affecting both. This study is a quantitative research with an actuarial modeling approach that aims to model the premium of unit-linked endowment life insurance based on stock investment using the annual ratchet method and Gompertz’s law. Stock returns and volatility are used as the basis for determining investment benefits under the annual ratchet method, using stock data for PT Bank Central Asia Tbk. The annual ratchet method is applied to protect the investment value from market declines by implementing cap and floor limits. Survival and mortality probabilities are modeled using Gompertz’s law. The results of the study show that, based on mortality modeling using Gompertz’s law and the annual ratchet mechanism, the net single premium for unit-linked endowment life insurance that must be paid at the beginning of the contract was Rp 129,098,509. These results show that applying the annual ratchet method can protect against fluctuations in investment value while accounting for mortality risk in premium determination, making the resulting model an alternative for developing more stable unit-linked life insurance products.
Analysis of Term Life Insurance Reserves Using the Full Preliminary Term and Fackler Method with an Extended Vasicek Interest Rate Based on Ordinary Least Square Aldila Nur Indah Berliana Ratam; Marisa Marisa
Parameter: Jurnal Matematika, Statistika dan Terapannya Vol 5 No 2 (2026): Parameter: Jurnal Matematika, Statistika dan Terapannya
Publisher : Jurusan Matematika FMIPA Universitas Pattimura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/parameterv5i2pp287-300

Abstract

Premium reserves have an essential role in maintaining financial sustainability and risk control in life insurance companies. This study aims to analyze the calculation of premium reserves for term life insurance products using the Full Preliminary Term (FPT) and the Fackler method. The FPT method has a relatively large acquisition cost at the beginning of the policy year, whereas Fackler applies long premium payments and generates different reserve patterns. Interest rate analysis uses the Extended Vasicek model, with parameter estimation via Ordinary Least Squares (OLS) based on Bank Indonesia interest rate data (BI rate) for 2010 – 2025. The results show that the FPT method generates more stable reserves at the beginning of the coverage period. In contrast, the Fackler method forms reserves more evenly throughout the premium payment period. The interest rates obtained from the Extended Vasicek model are relevant and can be applied in actuarial calculation practices. The data-based approach and statistical methods used in this study are expected to contribute both theoretically and practically, especially for actuaries and risk managers in decision-making related to the management of long-term liabilities in the life insurance industry.
Co-Authors Agus Irawan Marisa Marisa Marisa Nasrullah