Modification of The Lee-Carter Mortality Model And Its Application In The Pension Scheme

• Autorzy: Agnieszka Rossa
• Języki publikacji: EN

Abstrakty

EN

In this paper, a new approach to mortality forecasting is proposed based on an improved model of the Lee-Carter type. The standard Lee-Carter model and its modified version were introduced and compared using mortality data for Poland and some other European countries. Forecasts of log-central age-specific death rates were then derived and used to predict death probabilities and life expectancies for males and females in Poland, which are the main parameters of the so-called dynamic life tables (also known as mortality tables). The application of the proposed methodology in calculations of the present values of future pension annuities is presented in the article. Scenarios of monthly pensions obtained with the use of dynamic life tables were considered and compared with analogous scenarios based on the static (period) life tables published every year by the Central Statistical Office of Poland.(original abstract)

Słowa kluczowe

PL

Umieralność; Matematyczne modele umieralności; Emerytury; System emerytalny

EN

Mortality; Mathematical model of mortality; Pensions; Pension schemes

• Czasopismo: Argumenta Oeconomica
• Rocznik: 2022
• Numer: nr 2 (49)
• Strony: 93-113

Twórcy

autor

Agnieszka Rossa

• University of Lodz, Poland

Bibliografia

• Alho, J. M., Discussion of Lee (2002). North American Actuarial Journal, 4 (1), 91-93.
• Booth, H., Maindonald, J., Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline, Population Studies, 56, 325-336.
• Brouhns, N., Denuit, M., Van Keilegom, I. (2005). Bootstrapping the Poisson log-bilinear model for mortality forecasting, Scandinavian Actuarial Journal, 3, 212-224.
• Brouhns, N., Denuit, M., Vermunt, J. K. (a) (2002). A Poisson log-bilinear approach to the construction of projected life tables, Insurance: Mathematics and Economics, 31(3), 373-393.
• Brouhns, N., Denuit, M., Vermunt, J. K. (b) (2002). Measuring the longevity risk in mortality projections, Bulletin of the Swiss Association of Actuaries, 2, 105-130.
• Carter, L., (1996). Forecasting U.S. mortality: A comparison of Box-Jenkins ARIMA and structural time series models, The Sociological Quarterly, 37(7), 127-144.
• Danesi, I .L., Haberman, S., Millossovich, P. (2015). Forecasting mortality in subpopulations using Lee-Carter type models: A comparison, Insurance: Mathematics and Economics, 62(4), 151-161.
• Denuit, M., Dhaene, J. (2007). Nonmonotonic bounds of the survival probabilities in the Lee-Carter model for mortality projection, Journal of Computational and Applied Mathematics, 203, 169-176.
• Good, I. J. (1969). Some applications of the singular decomposition of a matrix, Technometrics, 11, 823-831.
• Trwanie życia 2020, Central Statistical Office, Warszawa, 2021, stat.gov.pl.
• Haberman, S., Renshaw, A.E. (2012). Parametric mortality improvement rate modelling and projecting, Insurance: Mathematics and Economics, 50(3), 309-333.
• Koissi, M. C., Shapiro, A. F., Högnäs, G. (2006). Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval, Insurance: Mathematics and Economics, 38(1), 1-20.
• Lee, R. D. (2000). The Lee-Carter method for forecasting mortality with various extensions and applications, North American Actuarial Journal, 4(1), 80-93.
• Lee, R. D., Carter, L. R. (1992). Modelling and forecasting U.S. mortality, Journal of American Statistical Association, 87(14), 659-675.
• Li, N., Lee, R., Tuljapurkar, S. (2004). Using the Lee-Carter method to forecast mortality for population with limited data, International Statistical Review,72 (1), 19-36.
• Lundström, H., Qvist, J. (2004). Mortality forecasting and trend shifts: an application of the Lee-Carter model to Swedish mortality data, International Statistical Review, 72(1), 37-50.
• OECD, Pensions at a glance 2019: OECD and G20 indicators, OECD Publishing, Paris, 2019.
• Renshaw, A. E., Haberman, S. (a) (2003). On the forecasting of mortality reduction factors, Insurance: Mathematics and Economics, 32(3), 379-401.
• Renshaw, A. E., Haberman, S. (b), (2003). Lee-Carter mortality forecasting. A parallel generalized linear modelling approach for England and Wales mortality projections, Applied Statistics, 52, 119-137.
• Renshaw, A. E., Haberman, S. (c), (2003). Lee-Carter mortality forecasting with age specific enhancement, Insurance: Mathematics and Economics, 33(2), 255-272.
• Rossa, A. (ed.), (2011). Analiza i modelowanie umieralności w ujęciu dynamicznym, Wydawnictwo UŁ, Łódź.
• Skałba, M. (2002). Ubezpieczenia na życie, WNT, Warszawa.
• Szumlicz, T. (ed.) (2007). Analiza ubezpieczeniowych implikacji wyników prognozy przeciętnego dalszego trwania życia uzyskanej metodą Lee-Cartera, Wiadomości Ubezpieczeniowe.
• Tuljapurkar, S., Nan, L., Boe, C. (2000). A universal pattern of mortality decline in the G7 countries, Nature, 405, 789-792.
• Trwanie życia w 2020 r., GUS, Warszawa, 2021. Received: April 2020, revised: January 2022

Identyfikatory

DOI

10.15611/aoe.2022.2.05