Calculation of Annual Premiums and Premium Reserves for Endowment Joint Life Insurance Based on Stochastic Interest Rates Using the Monte Carlo Method - Bela Cintiya Samwan; Agusyarif Rezka Nuha; Armayani Arsal; Emli Rahmi; La Ode Nashar (Sean Institute, 2026)
This study examines the determination of annual premiums and premium reserves for an endowment joint life insurance product by incorporating interest rate uncertainty through the Cox-Ingersoll-Ross (CIR) stochastic model and Monte Carlo simulation. The Indonesian Mortality Table 2023 is used to compute joint survival probabilities for the three insured individuals, while the CIR parameters are estimated from historical interest rate data for the period 2020-2024. The present value of benefits and annuities is calculated along each simulated path, enabling the premium and premium reserves to be evaluated prospectively based on fluctuating interest rate dynamics. The results show that the magnitude of premiums and reserves is influenced by the initial ages of the insured, the mortality structure, the sum assured, and the variability of the simulated interest rates. At the beginning of the contract, all scenarios produce negative reserves because accumulated premiums are still insufficient to cover the expected present value of benefits. However, the reserves increase steadily over time and turn positive toward the end of the insurance term. These findings indicate that the Monte Carlo approach based on the CIR model provides a more adaptive and realistic representation of premium and reserve behavior compared with deterministic methods, thereby supporting more accurate financial risk assessment for insurance companies.