Perhitungan net premium reserves produk multiple life dengan pemodelan survival copula berdasarkan selisih usia pasangan = Net premium reserves calculation of multiple life products using survival copulas based on the age difference of married couples

Oktavian, Grady Matthias (2020) Perhitungan net premium reserves produk multiple life dengan pemodelan survival copula berdasarkan selisih usia pasangan = Net premium reserves calculation of multiple life products using survival copulas based on the age difference of married couples. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Salah satu bentuk produk asuransi jiwa yang ditujukan untuk pasangan suami istri adalah produk multiple life. Terdapat berbagai macam skema pembayaran yang memungkinkan, namun secara umum, produk multiple life terbagi menjadi dua jenis, yaitu joint life dan last survivor. Pada produk joint life, uang pertanggungan dicairkan salah satu anggota pasangan meninggal dunia, namun pada last survivor, uang pertanggungan dicairkan setelah kedua pasangan meninggal dunia. Perusahaan asuransi harus mampu memodelkan mortalitas dari pihak tertanggung agar cadangan dana yang dimiliki perusahaan tidak kekurangan maupun terlalu berlebihan. Oleh karena itu, dibutuhkan pemodelan mortalitas pada pasangan suami istri. Pemodelan mortalitas ini berbeda dengan pemodelan mortalitas individu, sebab pasangan suami istri memiliki faktor dependensi yang memengaruhi mortalitas satu sama lain. Pemodelan mortalitas pasangan suami istri dilakukan dengan survival copula dari copula Archimedean Gumbel, Clayton, Frank, Joe, dan Ali-Mikhail-Haq. Pemodelan survival copula dilakukan tanpa melihat selisih usia suami istri dan dengan memperhitungkan selisih usia suami istri. Setelah dilakukan pemodelan menggunakan survival copula, dilakukan uji goodness of fit untuk menentukan mana survival copula terbaik. Survival copula Gumbel terpilih menjadi survival copula terbaik dan menjadi dasar perhitungan dana cadangan. Perhitungan dana cadangan dilakukan untuk tiga model, yaitu model dengan asumsi independensi, model survival copula Gumbel tanpa selisih usia, dan model survival copula Gumbel dengan selisih usia. Berdasarkan uji Kruskal Wallis yang dilakukan pada ketiga model tersebut, disimpulkan bahwa perbedaan yang signifkan antara model dengan asumsi independensi dan model survival copula terlihat pada pasangan yang usia istrinya lebih tua atau sama dengan usia suami. Namun, tidak terdapat perbedaan yang signifikan pada model dana cadangan yang dihitung dengan survival copula Gumbel tanpa selisih usia dan survival copula Gumbel dengan selisih usia. / One of life insurance products aimed at couples are called multiple life products. There are varying payment schemes of such products, however it is generally divided into two types, joint life and last survivor. Joint life products will give the benefit money if one of the individuals in the couple passed away, and multiple life products will give the benefit money if both the individuals in the couple has passed away. Actuaries in insurance companies should be able to model the mortality of couples in order to plan the reserves held by the company. However, modelling mortality for couples are not the same as modelling mortality for individuals. There is a dependency factor that affects the mortality of each individuals in the couple. Five Archimedean copula (in their survival copula form), Gumbel, Clayton, Frank, Joe and Ali-Mikhail-Haq are used to model the dependency factor of couple in the multiple life products. The modelling process is done twice, the first one does not include age difference as a factor to determine the survival copula’s dependency parameter, and the second model includes age difference among couples to determine the survival copula’s dependency parameter. Goodness of fit test is done to test which copula model is the most adequate, and it is found out that the Gumbel survival copula is the best Archimedean survival copula to model such dependency. Reserves calculation are done to create three models, the first model assumes dependency among individuals within the couple, the second model uses Gumbel survival copula without age difference, and the third model uses Gumbel survival copula with age difference. After comparing and testing these three models using Kruskal Wallis test, a significant difference between the model with dependency assumption and the survival copula models can be noticed in cases where the age of wife is more than or equal to the age of husband. However, there are no statistically significant difference between the survival copula model without age difference and the survival copula model with age difference.

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