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題名 台灣地區死亡率推估的實證方法之研究與相關年金問題之探討
作者 曾奕翔
貢獻者 余清祥
曾奕翔
關鍵詞 Mortality Improvement
Population Projection
Lee-Carter Method
Cross-validation
Simulation
Pure Premium
Annuity
1989 TSO
日期 2002
上傳時間 9-May-2016 16:30:57 (UTC+8)
摘要 　　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.
參考文獻 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.
描述 碩士
國立政治大學
風險管理與保險研究所
89358011
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2010000317
資料類型 thesis
dc.contributor.advisor 余清祥zh_TW
dc.contributor.author (Authors) 曾奕翔zh_TW
dc.creator (作者) 曾奕翔zh_TW
dc.date (日期) 2002en_US
dc.date.accessioned 9-May-2016 16:30:57 (UTC+8)-
dc.date.available 9-May-2016 16:30:57 (UTC+8)-
dc.date.issued (上傳時間) 9-May-2016 16:30:57 (UTC+8)-
dc.identifier (Other Identifiers) A2010000317en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/95557-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 89358011zh_TW
dc.description.abstract (摘要) 　　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.		en_US
dc.description.tableofcontents 謝詞
Abstract
目錄
表目錄
圖目錄
附錄目錄
第一章　前言-----1
　　第一節　研究動機與目的-----1
　　第二節　研究目標-----3
第二章　文獻探討與模型介紹-----4
　　第一節　Lee-Carter法-----4
　　第二節　多項式迴歸法-----7
　　第三節　多變量分析-----8
　　第四節　其它模型-----9
　　第五節　國內外實證研究-----12
第三章　實證與模擬分析-----16
　　第一節　資料來源與比較標準-----16
　　第二節　Lee-Carter模型的模擬研究-----16
　　第三節　分析結果的比較-----19
第四章　死亡率的改善與保險費率的關係-----22
　　第一節　相關的生命表資料-----23
　　第二節　年金保費的比較-----25
　　第三節　其他壽險保費的比較-----28
　　第四節　綜合比較-----30
第五章　結論與建議-----32
　　第一節　結論-----32
　　第二節　建議與未來研究方向-----33
參考文獻-----35

表目錄
表一：民國89年全民健保高齡及非高齡每人醫療費用比較-----2
表二：美國1933年到1987年的人口資料所配適的ax與bx值（男女混合）-----13
表三：曰本1951年到1990年的人口資料所配適的ax與bx值-----14
表四：台灣地區1950年至1997年的人口資料所配適的ax與bx值-----15
表五：MAPE預測能力等級區分-----16
表六：台灣地區人口的平均餘命（單位：歲）-----22

圖目錄
圖1：台灣1980-2000男性死亡率的對數曲線-----2
圖2：台灣地區歷年死亡資料紀錄（男性）-----17
圖3：Lee-Carter模型之配適方法模擬比較（左圖：男性；右圖：女性）-----18
圖4：各種方法的男性死亡率MAPE預測誤差比較-----19
圖5：各種方法的女性死亡率MAPE預測誤差比較-----20
圖6：利率7%在多變量法下男性三種支領年齡年金純保費低估比例-----27
圖7：利率7%在多變量法下男性三種投保年齡終身壽險純保費低估比例-----29

附錄目錄
附錄一：Lee-Carter模型的模擬研究參數-----37
附錄二：Lee-Carter配適方法模擬的MAPE與RMSPE-----39
附錄三：死亡率預測之MAPE與RMSPE比較-----40
附錄四：各種生命表（男性與女性）-----42
附錄五：各種模型假設下純養老險躉繳保費的低估百分比（男性與女性）-----48
附錄六：各種模型假設下純終身壽險躉繳保費的超收百分比（男性與女性）-----54
附錄七：各種模型假設下純生死合險躉繳保費的超收百分比（男性與女性）-----60
附錄八：多變量法下三種投保年齡終身壽險與年金保險保單銷售組合（男性與女性）-----66		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2010000317en_US
dc.subject (關鍵詞) Mortality Improvementen_US
dc.subject (關鍵詞) Population Projectionen_US
dc.subject (關鍵詞) Lee-Carter Methoden_US
dc.subject (關鍵詞) Cross-validationen_US
dc.subject (關鍵詞) Simulationen_US
dc.subject (關鍵詞) Pure Premiumen_US
dc.subject (關鍵詞) Annuityen_US
dc.subject (關鍵詞) 1989 TSOen_US
dc.title (題名) 台灣地區死亡率推估的實證方法之研究與相關年金問題之探討zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 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.		zh_TW