Perhitungan Premi Asuransi Joint-Life Menggunakan Tabel Mortalitas Lee–Carter dan Ketergantungan Archimedean Copula

Abstract

Asuransi jiwa joint-life memerlukan peluang hidup gabungan dua tertanggung dalam perhitungan premi. Penelitian ini bertujuan untuk menghitung premi bersih tahunan joint-life dengan menggabungkan proyeksi probabilitas kematian marginal model Lee–Carter dan struktur ketergantungan Archimedean copula. Data mortalitas diperoleh dari Human Mortality Database dengan identifikasi awal terhadap 50 populasi. Populasi Italia dipilih sebagai studi kasus karena menunjukkan variasi model ketergantungan yang serupa dengan variasi 50 populasi. Probabilitas kematian marginal pria dan wanita diproyeksikan sampai tahun 2026 menggunakan model Lee–Carter dengan indeks mortalitas yang mengikuti random walk with drift. Struktur ketergantungan dibentuk dari perubahan tahunan indeks mortalitas pria dan wanita serta diestimasi pada 24 rolling window berukuran 25 tahun menggunakan metode maximum pseudo-likelihood. Kesesuaian model dievaluasi menggunakan statistik Cramér–von Mises dengan 1000 replikasi bootstrap, kemudian model yang tidak ditolak dibandingkan berdasarkan AIC. Model Gumbel tidak ditolak pada seluruh window dan menjadi model dengan AIC terendah pada tujuh window terakhir. Pada lima pasangan usia, premi model Gumbel lebih rendah sebesar 14.34%–22.29% dibandingkan model independen. Analisis sensitivitas menunjukkan bahwa penggunaan batas bawah dan batas atas proyeksi mortalitas marginal menghasilkan perubahan premi dengan nilai parameter Gumbel yang tetap.

Joint-life insurance requires the joint survival probability of two insured lives in premium calculations. This study aims to calculates annual net premiums for joint-life insurance by combining Lee–Carter projections of marginal mortality probabilities with Archimedean copula dependence structures. Mortality data were obtained from the Human Mortality Database, with an initial identification of 50 populations. Italy was selected as the case study because its male and female mortality data showed variation in dependence models during the modern period. Male and female marginal mortality probabilities were projected to 2026 using the Lee–Carter model, with the mortality indices following random walks with drift. The dependence structure was constructed from annual changes in male and female mortality indices and estimated over 24 rolling windows of 25 years using maximum pseudo-likelihood. Model adequacy was evaluated using the Cramér–von Mises statistic with 1000 bootstrap replications, followed by AIC comparison among the models that were not rejected. The Gumbel copula was not rejected in any window and had the lowest AIC in the seven most recent windows. For the five age pairs, the Gumbel premiums were 14.34%–22.29% lower than the independence premiums. The sensitivity analysis showed that the lower and upper marginal mortality projections changed the premiums, while the Gumbel parameter was held constant.