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

Diserahkan: 5 Ogos 2017/Diterima: 10 Januari 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

RUJUKAN

Ahmadi, S.S. & Gaillardetz, P. 2015. Modeling mortality and pricing life annuities with Lévy processes. Insurance: Mathematics and Economics 64: 337-350.

Asmuni, N.H. 2015. Essays on annuities and their economic value for retirees. Ph.D. Thesis. Macquarie University Australia (Unpublished).

Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. & Nesbitt, C.J. 1997. SAT 472: Actuarial Mathematics. 2nd ed. Schaumburg, Illinois, United States: Society of Actuaries.

Box, G.E.P. & Jenkins, G.M. 1976. Time Series Analysis, Forecasting and Control. San Francisco: Holden Day.

Dowd, K., Blake, D. & Cairns, A.J. 2010. Facing up to uncertain life expectancy: The longevity fan charts. Demography 47(1): 67-78.

Gjonça, A., Tomassini, C. & Vaupel, J.W. 1999. Male-female differences in mortality in the developed world. Rostock: Max Planck Institute for Demographic Research. MPIDR Working Paper WP 1999-009.

Husin, W.Z.W., Zainol, M.S. & Ramli, N.M. 2015. Performance of the Lee-Carter state space model in forecasting mortality. In Proceedings of the World Congress on Engineering.2015. p1.

Husin, W., Zakiyatussariroh, W., Zainol, M.S. & Ramli, N.M. 2016. Common factor model with multiple trends for forecasting short term mortality. Engineering Letters 24(1).

Hyndman, R.J., Booth, H. & Yasmeen, F. 2013. Coherent mortality forecasting: The product-ratio method with functional time series models. Demography 50(1): 261-283.

Ibrahim, R.I. & Siri, Z. 2011. Methods of expanding an abridged life tables: Comparison between two methods. Sains Malaysiana 40(12): 1449-53.

Kamaruddin, H.S. 2015. Forecasting mortality rate of malaysia using lee-carter extension of hynman-ullah and booth-maindonald-smith and its statistical comparison analysis. In The 4th Abu Dhabi University Annual International Conference: Mathematical Science & its Applications.

Kjærgaard, S., Canudas-Romo, V. & Vaupel, J.W. 2016. The importance of the reference populations for coherent mortality forecasting models. In European Population Conference.

Lee, R.D. & Carter, L.R. 1992. Modeling and forecasting US mortality. Journal of the American Statistical Association 87(419): 659-671.

Li, J.S.H. & Hardy, M.R. 2011. Measuring basis risk in longevity hedges. North American Actuarial Journal 15(2): 177-200.

Li, N. & Lee, R. 2005. Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography 42(3): 575-594.

Li, S.H. & Chan, W.S. 2004. Estimation of complete period life Tables for Singaporeans. Journal of Actuarial Practice 11: 129-146.

Ngataman, N., Ibrahim, R.I. & Yusuf, M.M. 2016. Forecasting the mortality rates of Malaysian population using Lee-Carter method. In AIP Conference Proceedings, AIP Publishing 1750 (1): 020009.

Oeppen, J. & Vaupel, J.W. 2002. Broken limits to life expectancy. Science 296 (5570): 1029-1031.

Roy, A., Punhani, S. & Liyan, S. 2012. How Increasing Longevity Affects Us All ?: Market, Economic & Social Implications. London: Global Demographics and Pensions Research.

Shair, S.N., Yusof, A.Y. & Asmuni, N.H. 2017a. Evaluation of the product ratio coherent model in forecasting mortality rates and life expectancy at births by States. In AIP Conference Proceedings 1842(1): 030010.

Shair, S., Purcal, S. & Parr, N. 2017b. Evaluating extensions to coherent mortality forecasting models. Risks 5(1): 16.

Tengku Muda, T.M.M. 2017. Adequacy of employee provident fund due to longevity Malaysian. The international seminar on Islamic jurisprudence in contemporary society (Islac 2017). Mac 2017. ISBN: 978-967-0899-57-2.

United Nations. 2013. Department of Economic and Social Affairs. Population Division: World Population Prospects: The 2012 Revision.

Villegas Ramirez, A. 2015. Mortality: Modelling, socio-economic differences and basis risk. City University London: Ph.D. Thesis. (Unpublished).

Wolf, R. 2013. What's happening in Malaysia: Getting prepared for retirement? Allianz International Pensions, (August), 1–11. www.projectm-online.com/research.

*Pengarang untuk surat-menyurat; email: fadhilahy@utm.my