Premium Sufficiency Reserve of Last Survivor Endowment Life Insurance Using Exponentiated Gumbel Distribution

Life insurance is a protection effort provided by the insurer against risks to the insured’s life that will arise from an unpredictable event. Insurance companies are required to prepare reserves to fulfill the sum insured when a claim occurs. Premium sufficiency reserves are modified reserves whose calculations use gross premiums that contain administrative maintenance costs. The purpose of this study is to determine the amount of premium sufficiency reserves of endowment life insurance for two insurance participants aged x years and y years using the exponentiated Gumbel distribution. The parameters of the exponentiated Gumbel distribution are estimated using the maximum likelihood method and then determined by a Newton-Raphson iteration method. The solution of the problem is obtained by determining the initial life annuity term, single premium, and annual premium so as to obtain the reserve formula of the premium sufficiency of the last survivor status endowment life insurance using the exponentiated Gumbel distribution. The results of the calculation of reserves premium sufficiency of endowment life insurance last survivor status using the exponentiated Gumbel distribution is slightly smaller than premium sufficiency reserve for endowment life insurance using the Indonesian Mortality Table 2019.