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All Journal Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika
Aldila Nur Indah Berliana Ratam
Sumatera Institute of Technology
Mathematics

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Term Life Insurance Reserves Using the Extended Vasicek Interest Rate Model with Fackler and Full Preliminary Term Methods Marisa; Aldila Nur Indah Berliana Ratam
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 9 No. 1 (2026): Volume 9 Nomor 1 Tahun 2026
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v9i1.8048

Abstract

Term life insurance reserve calculations are strongly influenced by interest rate uncertainty, which affects the present value of long-term liabilities. This study estimates term life insurance reserves using a stochastic interest rate approach based on the Extended Vasicek model, chosen for its mean-reverting property and analytical tractability, which allow it to capture interest rate dynamics in a stable and interpretable manner. The model parameters are estimated using the Jackknife resampling method to improve stability. The data used consist of the annual average BI Rate from 2010 to 2025 and the Indonesian Mortality Table 2019 (TMI 2019). The results suggest that the Jackknife-based Extended Vasicek model produces stable mean-reverting projections of interest rates. These projections are then applied to reserve calculations using the Fackler and Full Preliminary Term (FPT) methods. The findings indicate that the Fackler method generates a gradual reserve pattern that peaks mid-term before declining to zero. In contrast, the FPT method yields zero reserves in the first year, followed by higher accumulation in subsequent years. Overall, this approach provides relatively stable and realistic reserve estimates under stochastic interest rate conditions. From a practical perspective, the Extended Vasicek model may be considered an alternative framework for actuaries to model interest rate uncertainty in reserve calculations. Future research could further examine its performance under different economic scenarios or compare it with other stochastic interest rate models to better understand its applicability and limitations.
Co-Authors Marisa