Last-Survivor Insurance Premium and Benefit Reserve Calculation using Gamma-Gompertz Mortality Law

Abstract

When the insurance benefit of a last-survivor insurance product is payable at the moment of the last insured death, exploring continuous mortality models is essential to obtain the most appropriate premium and benefit reserve. In this study, Gamma-Gompertz mortality law was applied to Indonesian population mortality data at adulthood and old age stages to calculate the annual gross premium and gross benefit reserve of a whole life last survivor insurance product. The annual gross premium was computed using the actuarial equivalence principle. Results show that the older the policyholders purchase the product, the higher the annual gross premium they must pay. The gross benefit reserve needed to be set by the insurance company for the whole life last survivor insurance product was calculated using the prospective method. Its value grows for each valuation year until it approaches the insurance benefit amount.

Keywords

• annual gross premium, equivalence principle, gamma-gompertz mortality law, gross benefit reserve, last-survivor insurance, prospective method.