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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
Received: 9 October 2019/Accepted:
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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*Corresponding
author; email: zamira@ukm.edu.my
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