Sains Malaysiana 49(8)(2020): 2013-2022

http://dx.doi.org/10.17576/jsm-2020-4908-24

Comparing and Forecasting using Stochastic Mortality Models: A Monte Carlo Simulation

(Perbandingan dan Peramalan menggunakan Model Kematian Stokastik: Suatu Simulasi Monte Carlo)

ZAMIRA HASANAH ZAMZURI* & GWEE JIA HUI

Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Diserahkan: 9 Oktober 2019/Diterima: 16 April 2020

ABSTRACT

Generalized Age-Period-Cohort Model (GAPC) has been widely accepted as a mean of modelling mortality improvement but the parameter risk associated with it raises problem on forecasting accuracy. Hence, this study aims to  utilise the simulation strategy to account for variability and uncertainty in the point and interval mortality estimate by using mortality experience of Taiwan. This study also aim to identify the best mortality model for Taiwan data and further compute the ruin probability to assess the solvency risk. The results show that the error of point estimate could be minimized using simulation depending on the type of forecast statistics and models. The interval estimates on the other hand generally produce similar width in most cases as compared to those without using simulation, suggesting that simulation failed to increase forecast accuracy significantly in terms of interval estimate with exception on Haberman-Renshaw model with cohort effect in squared form (HRb) in high age female population projection. Age-Period-Cohort (APC) model is found to be most suited to both gender population in Taiwan by focusing on its ability to generate biological plausible rate, goodness of fit and forecasting performance. The mortality forecast based on APC model is then used in virtual cash flow projection on an annuity portfolio. Result shows that Renshaw-Haberman (RH) model is more sensible in annuity pricing as its product produce least solvency risk besides showing that the risk is greatly contributed by women population of higher age in the case of Taiwan.

Keywords: Generalized Age-Period-Cohort Model; parameter uncertainty; simulation; solvency risk

ABSTRAK

Model Umur-Tempoh-Kohot Teritlak (GAPC) telah luas digunakan untuk memodelkan penambahbaikan kematian tetapi wujud risiko ketidaktentuan parameter terhadap hasil unjuran model tersebut. Oleh yang demikian, kajian ini bermatlamat untuk mengaplikasikan konsep simulasi dengan mengambil kira kepelbagaian dan ketidakpastian dalam anggaran titik dan selang bagi data Taiwan. Kajian ini juga bertujuan untuk mengenal pasti model kematian terbaik untuk data Taiwan seterusnya menghitung kebarangkalian kemusnahan untuk menilai risiko kesolvenan. Hasil kajian menunjukkan bahawa kaedah simulasi Monte Carlo berupaya meminimumkan lagi ralat pelunjuran untuk statistik dan model tertentu pada anggaran titiknya. Namun, kebanyakan selang hasilnya pula adalah lebih kurang sama dengan hasil tanpa simulasi, maka tidak memberi anggaran selang yang terbukti lebih jitu untuk kebanyakan kes kecuali model Haberman-Renshaw dengan kesan kohort dalam bentuk kuasa dua (HRb) pada populasi wanita berumur tinggi. Model APC (Age-Period-Cohort) sesuai untuk melunjurkan kematian masa depan populasi lelaki dan perempuan di Taiwan dengan tumpuan terhadap keupayaannya menghasilkan unjuran yang munasabah dari segi biologi, kebagusan penyuaian serta prestasi pelunjuran. Pelunjuran pengaliran kewangan portfolio anuiti menunjukkan bahawa portfolio yang ditentuharga oleh model Renshaw-Haberman (RH) mengundang risiko kesolvenan yang paling rendah dan populasi wanita berumur tua memberi sumbangan terbesar terhadap risiko ini dalam kes Taiwan.

Kata kunci: Ketidaktentuan parameter; Model Umur-Tempoh-Kohot Teritlak; risiko kesolvenan; simulasi

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*Pengarang untuk surat-menyurat; email: zamira@ukm.edu.my