Cost Component Calculation for Endowment Insurance Premiums on Multiple Life Using the Gompertz Distribution

Abstract

This study aims to develop a gross premium model for endowment insurance products under a multiple life setting by incorporating various actual cost components and applying the Gompertz mortality distribution. The proposed model includes acquisition costs at the beginning and end of the first policy year, premium collection costs, and annual policy maintenance costs, all of which are calculated based on present values of benefits and annuities. Parameter estimation is conducted using linear regression with a bounded optimization approach, where all parameters are constrained to be strictly positive to reflect realistic conditions in insurance practice. The simulation results yield parameter estimates of  a₁=0,97074,  a₂=0,912217, β=Rp 19.344,46 and γ=Rp 20.105,23 which are considered actuarially reasonable. The high coefficient of determination, , R²=98,46%, indicates that the model has an excellent fit to the gross premium data. This research demonstrates that an actuarial-based cost formulation combined with statistical estimation can serve as an effective and transparent approach in determining premiums for endowment life insurance products with more than one insured.