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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika
Johan, Arsyelina Husni
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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WHOLE LIFE INSURANCE UTILIZING THE COMMISSIONERS METHOD AND THE VASICEK INTEREST RATE MODEL FOR PREMIUM RESERVE ANALYSIS Romantica, Krishna Prafidya; Johan, Arsyelina Husni; Jayanegara, Anuraga; Leo, Jason Filbert
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1001-1018

Abstract

Premium reserves play a vital role in ensuring that insurance firms can meet their future obligations to policyholders. Traditional fixed-rate approaches often fail to reflect market volatility, leading to potential misestimations. This study addresses this gap by integrating the Commissioners Method with the Vasicek stochastic interest rate model to evaluate premium reserves for whole life insurance. The research hypothesizes that the Vasicek model provides more realistic reserve estimates than fixed-rate models, that payment frequency and behavioral preferences significantly affect reserve levels, and that gender-specific mortality impacts reserve adequacy. Using BI-7D-RR interest rate data from 2019–2024, Vasicek parameters were calibrated and applied to reserve calculations. A sensitivity analysis was conducted by varying the model’s mean reversion, volatility, and long-term mean parameters. The results confirm that Vasicek-based reserves are more robust and realistic than fixed-rate estimates. Incorporating a DARA utility function adds behavioral realism, while payment frequency strongly influences reserve accumulation. Gender-specific mortality produces systematically higher reserves for male policyholders. Sensitivity analysis highlights the model’s robustness, with reserves responding predictably to parameter changes. This research contributes theoretically by linking stochastic modeling, demographics, and behavioral economics, while providing practical guidance for insurers to strengthen reserve adequacy and financial resilience under uncertainty.
Endowment Life Insurance Calculation Modeling with DARA Utility Function and Stochastic Interest Leo, Jason Filbert; Romantica, Krishna Prafidya; Johan, Arsyelina Husni
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 11 No. 1 (2026): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v11i1.993

Abstract

In this research, a 10-year endowment life insurance’s premium will be calculated with a DARA function according to principle of utility equivalence. The calculation results will be performed using a Vasicek interest-based model, among male and female policyholders within the age range of 20-80 years old, and over varying benefit levels. Indonesian Mortality Table IV 2019 is used as reference for mortality data. Stochastic interest is modeled using the Vasicek Model derived through Ordinary Least Square Method (OLS) Method from BI-Rate in the volatile September 2022 - August 2024 period with a monthly step time, which yields the following parameters: , , , resulting in a 95% confidence interval  with standard error . This  indicated high uncertainty in the interest modelling. The results showed that premium rate is heavily affected by this volatility in the interest rates. Premium value is higher for male than female policyholders and it increases faster at higher entry age due to an increase of the mortality rate. The relation between the DARA coefficient and premium value is non-linear despite a slight increase in premium when a larger coefficient is chosen. An increase of benefit rate is followed by a nearly proportional increase of the premium rate. Further research on this topic could analyze the impact of policy horizon and wealth on the premium rate or compare the results with another stochastic model (e.g. CIR model).
Co-Authors Anuraga Jayanegara Leo, Jason Filbert Romantica, Krishna Prafidya