Future Life-Tables Based on the Lee-Carter Methodology and their Application to Calculating the Pension Annuities

• Autorzy: Agnieszka Rossa
• Języki publikacji: EN

Abstrakty

EN

In the paper a new recursive approach to the mortality forecasting is proposed based on the well-known Lee-Carter stochastic model. The standard Lee-Carter method and its modified version are presented and compared using mortality data for Poland in the time period 1990-2007. The results obtained indicate that the recursive approach gives more accurate forecasts in terms of the mean squared error. Stochastic forecasts of age-specific death rates are also used to predict death probabilities and life expectancy being the main parameters of the life-tables. As an example, future life-tables for 2020 are calculated. Applications of Lee-Carter methodology in pension annuity calculations are presented. (original abstract)

Słowa kluczowe

EN

Population; Pensions; Demographic structure; Lee-Carter model; Demographic forecasts; Mathematical model of mortality; Mortality statistics

PL

Ludność; Emerytury; Struktura demograficzna; Model Lee-Cartera; Prognozy demograficzne; Matematyczne modele umieralności; Statystyka umieralności

• Czasopismo: Acta Universitatis Lodziensis. Folia Oeconomica
• Rocznik: 2011
• Tom: 250 Demographic Future of Poland
• Strony: 31--50

Twórcy

autor

Agnieszka Rossa

• University of Lodz, Poland

Bibliografia

• Alho J. M., 2000, Discussion of Lee (2000), North American Actuarial Journal, 4(1), 91-93.
• Bomsdorf E., 2004, Life expectancy in Germany until 2050, Experimental Gerontology, 39, 159-163.
• 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, Scandinnavian Actuaria/Journal, 3, 212-224.
• Brouhns N., Denuit M., Vermunt J. K., 2002a, A Poisson log-bilinear approach to the construction of projected lifetables, Insurance: Mathematics and Economics, 31 (3), 373-393.
• Brouhns N., Denuit M., Vermunt J. K., 2002b, Measuring the longevity risk in mortality projections, Bulletin of the Swiss Association of Actuaries, 2, 105-130.
• Blaschke E., 1923, Sulle tavole di mortalita variabili col tempo, Giornale di Mathematica Finanziara, 5, 1-31.
• Carter L., 1996, Forecasting U.S. mortality: a comparison of Box-Jenkins ARJMA and structural time series models, The Sociological Quarterly, 37 (7), 127-144.
• 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.
• 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.
• Renshaw A. E., Haberman S., 2003a, On the forecasting of mortality reduction factors, Insurance: Mathematics and Economics, 32 (3), 379-401.
• Renshaw A. E., Haberman S., 2003b. 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., 2003c, Lee-Carter mortality forecasting with age specific enhancement, Insurance: Mathematics and Economics, 33 (2), 255-272.
• 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.
• Wilmoth J. R., Horiuchi S., 1999, Rectangularization revised: variability of age at death within human populations, Demography, 36 (4), 475-495.

Identyfikatory

DOI

11089/605