Porovnanie stochastických modelov úmrtnosti na údajoch Slovenska
Klíčová slova:
Vekovo špecifická centrálna miera úmrtnosti, Lee-Carterov model, CBD model, Metóda Habermana a Russoliloa, Metóda najmenších štvorcov, ARIMAAbstrakt
Cieľom príspevku je porovnanie dvoch najznámejších stochastických modelov úmrtnosti – Lee-Carterov (LC) model a Cairns-Blake-Dowdov (CBD) model, s využitím údajov o úmrtnosti populácie Slovenska. Údaje o úmrtnosti pochádzajú zo stránky mortality.org a pokrývajú obdobie od vzniku Slovenskej republiky (1993) do roku 2017. Na odhad parametrov modelov bola použitá metóda najmenších štvorcov a tiež metóda Habermana a Russoliloa. Na prognózovanie časovo závislých parametrov bol aplikovaný model autoregresného integrovaného kĺzavého priemeru ARIMA. Prognóza úmrtnosti je stanovená na najbližšie tri roky. Výsledky boli jednoducho numericky a graficky porovnané a ukazujú rozdiely medzi modelmi, ktoré dokazujú výskyt modelovaného rizika.Reference
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2. Cairns, A. J., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Khalaf-Allah, M.: Mortality density forecasts: An analysis of six stochastic mortality models. Insurance: Mathematics and Economics 48.3, 355-367, (2011).
3. Chavan, R., Ramkrishna, S.: Modeling and Forecasting Mortality Using the Lee-Carter Model for Indian Population Based on Decade-wise Data. Sri Lankan Journal of Applied Statistics 17.1 (2016).
4. Haberman, S., Russolillo, M.: Lee Carter mortality forecasting: application to the Italian population. Actuarial Research Paper No. 167, Cass Business School, London (2005).
5. Heligman, L., Pollard, J. H.: The age pattern of mortality. Journal of the Institute of Actuaries 107.1 (1980).
6. Human Mortality Database, mortality.org
7. Jiang, L.: Changing kinship structure and its implications for old-age support in urban and rural China. Population Studies 49.1 (1995).
8. Koissi, M., Shapiro, A. F., Högnäs, G.: Evaluating and extending the Lee–Carter model for mortality forecasting: Bootstrap confidence interval. Insurance: Mathematics and Economics 38.1 (2006).
9. Lee, R. D., Carter, L. R.: Modeling and forecasting US mortality. Journal of the American statistical association 87.419 (1992).
10. Lee, R.: The Lee-Carter method for forecasting mortality, with various extensions and applications. North American actuarial journal 4.1 (2000).
11. McNown, R., Rogers A.: Forecasting mortality: A parameterized time series approach. Demography 26.4 (1989).
12. Milevsky, M. A., Promislow, S. D.: Mortality derivatives and the option to annuitise. Insurance: Mathematics and Economics 29.3 (2001).
13. Nocito, S.: Stochastic Mortality Projections: A Comparison of the Lee-Carter and the Cairns-Blake-Dowd models Using Italian Data. University of Studies of Turin (2015).
14. Pitacco, E., Denuit, M., Haberman, S., Olivieri, A.: Modelling longevity dynamics for pensions and annuity business. Oxford University Press (2009).
15. Safitri, Y. R., Mardiyati, S., Malik, M.: The Cairns-Blake-Dowd model to forecast Indonesian mortality rates. In AIP Conference Proceedings (Vol. 2168, No. 1, p. 020039). AIP Publishing LLC (2019).
16. SAS Institute Inc: "SAS/ETS® 13.2 User’s Guide – The ARIMA procedure". Cary, NC: SAS Institute Inc (2014)
17. Singh, A., Ram, F.: Forecasting mortality in India. Population, Health and Development in India: Changing Perspective, TK Roy, M. Guruswamy, and Arokiaswamy, Rawat Publication Mumbai, India (2004).
18. Šoltésová, T.: Aktuárske modelovanie v životnom poistení. 1. vydanie. Bratislava: Vydavateľstvo Letra Edu. (2019).
19. Wilmoth, J. R.: 13 Mortality Projections for Japan. Health and mortality among elderly populations (1996).
20. Yadav, A., Yadav, S., Kesarwani, K.: Decelerating mortality rates in older ages and its prospects through Lee-Carter approach. PloS one 7.12 (2012).
