Penentuan Premi Tahunan Asuransi Jiwa Berjangka Last Survivor dengan Model Copula Generalized-Farlie-Gumbel-Morgenstern Tipe I dan II

Abstract

Asuransi jiwa last survivor merupakan salah satu contoh asuransi multi life (dua atau lebih tertanggung) di mana kegagalan terjadi ketika semua tertanggung telah meninggal dunia. Risiko kematian tertanggung berpengaruh dalam perhitungan premi tahunan. Perhitungan premi biasanya dilakukan dengan mengasumsikan kebebasan antar tertanggung, namun, dalam kenyataannya kerap kali pasangan suami istri memiliki risiko bersama. Keterkaitan risiko kematian suami terhadap istri dapat berbeda dengan keterkaitan risiko kematian istri terhadap suami. Dengan demikian, keterkaitan risiko kematian suami istri adalah asimetris. Pada karya ilmiah ini, dilakukan perhitungan premi tahunan asuransi jiwa berjangka n-tahun status last survivor bagi pasangan suami istri dengan asumsi kebebasan mortalitas dan asumsi ketakbebasan mortalitas model copula Generalized FarlieGumbel-Morgenstern (GFGM) tipe I sebagai copula simetris serta model copula GFGM tipe II sebagai copula asimetris. Berdasarkan perhitungan, premi tahunan yang dihitung menggunakan copula asimetris lebih besar daripada copula simetris maupun asumsi kebebasan mortalitas. Premi tahunan yang dihitung menggunakan copula simetris lebih besar daripada asumsi kebebasan.

Last-survivor life insurance is an example of multi-life insurance (two or more insureds) in which failure occurs if all insureds have died. The risk of death of the insureds influences the determination of the annual premium. Premiums calculations are usually carried out by assuming independence among the insureds, however, in reality, husband and wife often share the risk. The correlation between the risk of death of a husband to his wife may differ from that of a wife to her husband. Therefore, the correlation between the risk of death of husband and wife is asymmetric. In this scientific paper, the annual premiums for n-year term life insurance with last survivor status for married couples are calculated using the assumption of independent mortality and dependent mortality using the type I Generalized-Farlie-Gumbel-Morgenstern (GFGM) copula as symmetrical copula and the type II GFGM copula as asymmetrical copula. Based on calculation results, the annual premium determined by the asymmetrical copula is greater than the symmetrical copula and independent mortality. The annual premium determined by symmetrical copula is greater than the independent mortality.