Sains Malaysiana 47(6)(2018): 1337–1347

http://dx.doi.org/10.17576/jsm-2018-4706-31

Multi-Population Mortality Model: A Practical Approach

(Model Kematian Berbilang Populasi: Suatu Pendekatan Praktik)

SITI ROHANI MOHD NOR, FADHILAH YUSOF* & ARIFAH BAHAR

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor Darul Takzim, Malaysia

Received: 5 August 2017/Accepted: 10 January 2018

ABSTRACT

The growing number of multi-population mortality models in the recent years signifies the mortality improvement in developed countries. In this case, there exists a narrowing gap of sex-differential in life expectancy between populations; hence multi-population mortality models are designed to assimilate the correlation between populations. The present study considers two extensions of the single-population Lee-Carter model, namely the independent model and augmented common factor model. The independent model incorporates the information between male and female separately whereas the augmented common factor model incorporates the information between male and female simultaneously. The methods are demonstrated in two perspectives: First is by applying them to Malaysian mortality data and second is by comparing the significance of the methods to the annuity pricing. The performances of the two methods are then compared in which has been found that the augmented common factor model is more superior in terms of historical fit, forecast performance, and annuity pricing.

Keywords: Augmented; independent; Lee-Carter; mortality; Stochastic model

ABSTRAK

Peningkatan bilangan model kematian berbilang populasi sejak kebelakangan ini menandakan penambahbaikan tahap kematian di negara maju. Dalam kes ini, terdapat jurang kecil perbezaan seks dalam jangka hayat antara populasi, maka model kematian berbilang populasi direka untuk mengasimilasi hubungan antara populasi. Kajian ini mempertimbangkan dua lanjutan model tunggal populasi Lee-Carter, iaitu model bebas dan model faktor umum yang diperkukuhkan. Model bebas menggabungkan maklumat antara lelaki dan perempuan secara berasingan manakala model faktor umum yang diperkukuhkan menggabungkan maklumat antara lelaki dan perempuan secara serentak. Kaedah ini dapat ditunjukkan dalam dua perspektif: Pertama adalah dengan menggunakannya untuk data kematian Malaysia dan kedua adalah dengan membandingkan kepentingan kaedah dengan penentuan harga anuiti. Prestasi kedua-dua kaedah itu kemudiannya dibandingkan dan telah didapati bahawa model faktor umum yang diperkukuhkan adalah lebih tinggi daripada segi kesesuaian sejarah, prestasi ramalan dan penentuan harga anuiti.

Keywords: Bebas; diperkukuhkan; Lee-Carter; kematian; model stokastik

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*Corresponding author; email: fadhilahy@utm.my