Analysis of Term Life Insurance Premium Reserves Using the Zillmer Method with Hull–White Interest Rates - Fatahillah Akmal; Riaman; Nurul Gusriani (International Journal of Business, Economics, and Social Development, 2026)
This study analyzes the valuation of premium reserves for term life insurance using the Zillmer method under a stochastic interest rate framework. In conventional actuarial practice, premium reserves are commonly calculated using deterministic interest rate assumptions, which may inadequately reflect the dynamic nature of interest rate movements over long-term policy horizons. To address this limitation, this study applies the one-factor Hull–White interest rate model to incorporate stochastic interest rate dynamics into the reserve calculation process. The Hull–White model parameters are estimated using historical interest rate data, and interest rate paths are generated through numerical simulation. These simulated interest rates are then employed to compute discount factors in the calculation of Zillmer premium reserves. The analysis focuses on illustrating how stochastic interest rate movements influence the development of premium reserves over the policy duration, rather than on probabilistic risk measurement or capital adequacy assessment. The results show that premium reserves calculated under the stochastic interest rate framework exhibit dynamic patterns over time, particularly during the early and middle policy periods. Compared to deterministic interest rate assumptions, the stochastic approach captures variations in reserve values arising from interest rate fluctuations. This finding highlights the sensitivity of Zillmer premium reserves to interest rate dynamics. Overall, this study demonstrates that integrating the Hull–White stochastic interest rate model with the Zillmer method provides a descriptive and flexible framework for analyzing premium reserves in term life insurance. The proposed approach may serve as a basis for further research on stochastic valuation methods in actuarial applications.