In Taiwan area, the mortality rates at all ages have decreased since the end of World War II, and the life expectancy of people has increased from 62 in 1950's to 75 in 2000, which is an increase of 21%. The mortality improvement of the elderly (i.e. people ages 65 and over) is especially significant, which effects in the rapid population aging in Taiwan area. For example, the proportion of the elderly has increased from 6.14%in 1990 to 8.52% in 2000. On one hand, the prolonged life span for an individual means a longer period of retirement life and thus a larger retirement fund. On the other hand, a longer life for the government is equivalent to a more thorough social system for the elderly. Therefore, a reliable mortality rates projection is essential to both personal financial and social welfare planning.
　　In this study, we have two main objectives: First, we explore some frequent used models, such as Lee-Carter, multivariate regression and principal component methods. We use the data between 1950 to 1995 as the pilot data and 1996 to 2000 as the test data to judge which method has the smallest prediction error. In addition, based on computer simulation, we also evaluate the performance of the estimation methods for the Lee-Carter method. The second part (and the other objective) of this study is to explore the effect of mortality improvement on the pure premium of annuity insurance. In particular, we calculate the pure premium of the annuity under the best model acquired from the first part, and compare those under 1989 TSO and other life tables. We found that the pure premiums under current life tables are under estimated, which may cause the insolvency of insurance companies.

中文部分
內政部統計處(1963-2000)中華民國台閩地區人口統計。
余清祥(1997)修勻：統計在保險的應用，台北：雙葉。
周世宏(2001)台灣地區死亡率參數模型之研究，逢甲大學統計與精算研究所碩士論文。
張正鵬(1998)台灣地區高齡人口死亡率之預測，國立政治大學統計研究所碩士論文。
余清祥與連宏銘(1999),台灣地區死亡率現況的實證研究,壽險季刊。
人壽保險商業同業公會(2000) 人壽保險業務統計年報。
英文部分
Alho, M. J. (1989), Relating changes in life expectancy to changes in mortality, Demography, 26: 705-709.
Boe, C. and Tuljapurkar, S. (1998), Mortality change and forecasting: how much and how little do we know?, North American Actuarial Journal,2(4):13-47.
Booth, H., Maindonald, J., and Smith, L. (2001), Age-time interactions in mortality projection: applying lee-carter to Australia, Working papers in Demography, 85: 1-29.
Carter, L. R. and Lee, R. D. (1992), Modeling and forecasting U.S. mortality, Journal of the American Statistical Association, 87(419): 659-675.
Coale, A. J. and Horiuchi, S. (1990), Age patterns of mortality for older women: an analysis using the age-specific rate of mortality change with age, Mathematical Population Studies, 2(4): 245-267.
Hannerz, H. (2001), An extension of relational methods in mortality estimation, Demography Research, 26: 337-367.
Himes, L. C., Preston, S. H., and Condran, G. A. (1994), A relational model of mortality at older ages in law mortality countries, 48: 269-291.
Keyfitz, N. (1982), Choice of function for mortality analysis: effective forecasting depends on a minimum parameter representation, Theoretical Population Biology, 21: 329-352.
Lee, R. D. (2000), The lee-carter method for forecasting mortality, with various extensions and applications, North American Actuarial Journal, 4: 80-93.
Miller, T. and Lee, R. D. (2001), Evaluating the performance of lee-carter mortality forecasts, Demography, 38(4): 537-549.
Olshansky, S. J. (1988), On forecasting mortality, The Milbank Quarterly, 66: 482-530.
Pollard, J. H. (1987), Projection of age-specific mortality rates, Population Bulletin of the United Nations, 21 (22): 55-69.
Prskawetz, A. and Carter, L. R. (2001), Examining structural shifts in mortality using the lee-carter method, MPIDR WORKING PAPER WP 2001-007, 1-16.
Wilmoth, J. (1996), Mortality projections for Japan: a comparison of four methods, in Caselli, G. and Lopez, A. D. (eds.), Health and Mortality Among Elderly Populations, New York: Oxford University Press, 266-287.
Wilmoth, J. (1993), Computational methods for fitting and extrapolating the lee-carter model of mortality change, Technical Report, Department of Demography, University of California, Berkeley.
Yuen, K. C. (1997), Comments on some parametric models for mortality tables, Journal of Actuarial Practice, 5: 253-266.
Yue, C. J., Hu, Y., and Chang, C. (2000), A ratio method for old age mortality projection based on incomplete data: the case in Taiwan, Journal of Population Studies, 21: 1-16.