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題名 死亡壓縮與長壽風險之研究
A Study of Mortality Compression and Longevity Risk
作者 謝佩文
Hsieh, Pei Wen
貢獻者 余清祥
謝佩文
Hsieh, Pei Wen
關鍵詞 死亡壓縮
生存曲線矩形化
數值優化
電腦模擬
壽險保費
Mortality Compression
Rectangularization of Survival Curve
Optimization
Computer Simulation
Pure Premium
日期 2012
上傳時間 11-Jul-2013 16:58:17 (UTC+8)
摘要 醫療技術的進步以及生活品質的提升，預計人類平均壽命將持續延長，以臺灣為例，男、女性平均壽命將從2011年的75.98歲、82.65歲，增加到2060年的82.0歲、88.0歲（資料來源：行政院經濟建設委員會2012年推估）。壽命延長意謂更長的退休生活，世界各國在21世紀均面對需求日殷的老年生活照顧，包括退休金制度以及老人醫療等，這些社會福利及保險勢必增加國家財務負擔，因此壽命是否繼續延長或存有極限成為大家關心的議題。近年來，不少研究透過死亡壓縮(Mortality Compression)連結壽命議題，亦即探討死亡年齡是否將集中至更窄的範圍，但因為資料及研究方法的限制，死亡壓縮是否成立仍無定論。
本研究以統計方法、分配假設、資料品質，三個面向來探討死亡壓縮與延壽之間的關係。本研究提出三種數值優化方法：加權最小平方法(Weighted Least Squares；WLS)、非線性極值法(Nonlinear-Maximization；NM)及最大概似估計法(Maximal Likelihood Estimation；MLE)，透過電腦模擬衡量方法優劣，與過去常見的方法比較（Kannisto的SD(M+)），探討何者具有較小的均方誤差(Mean Squared Error；MSE)。其次若死亡年齡之真實死亡分配為t分配時，探討以常態假設代入計算所產生的偏誤；最後則是套入各國實際死亡資料，使用上述較佳的估計方法，檢視死亡壓縮是否存在。
研究結果顯示，NM具有不偏性質且具有較小的均方誤差，過去研究常用的SD(M+)反而有明顯偏誤，且隨著觀察值越多變異數反而增加。而若真實死亡分配若為t分配時，以原先利用常態假設所計算的年金險保費皆有低估的情形，分配的重要性可見一斑，進而探討在實務上常態分配之假設，發現與仍與實際情形有明顯之差異，不論是NM及SD(M+)在死亡壓縮的探討下，皆受到資料的限制而有待商榷。
Due to the advance in medical technology and the change of life style, the human life expectancy has been increasing since the end of the Second World War II and it is expected to continue the pace of increment. Longer life expectancy also means a longer life after retirement. People living in the 21st century are faced with growing demand for the retirement life, such as the pension funds and medical needs to the individuals, as well as the social welfare and insurance for the elderly to the government. Thus, the issue whether the lifespan has a limit receives a lot of attention. In particular, many studies focus on the topic of mortality compression, which means that the expectancy of lifespan has a limit and variance of lifespan converge. However, due to the availability of elderly data, there is still no consensus if the mortality compression is true.
In this study, we propose estimation methods to estimate modal age and variance of the age-at-death. Three types of methods are involved: weighted least squares (WLS) method, nonlinear maximization (NM) method, and maximum likelihood estimation (MLE) method, and they are compared to the method proposed by Kannisto, namely SD(M+), in 2000. We found that the NM method has a smaller MSE, and we cannot decide the mortality compression is true based on the data from Human Mortality Database. We also applied the normality and t distribution assumption to the age-at-death and compute the pure premiums for annuity products. We found that normality distribution would produce larger premiums than using the empirical mortality rates. Similarity, the bankruptcy probability would be higher if the t distribution is used.
參考文獻 中文部分：
王德睦與李大正，2009，台灣的存活曲線矩型化與壽命延長，人口學刊，36：1-31。
李明峰，2012，死亡壓縮與延壽之研究，國立政治大學統計學系碩士論文。

英文部分：
Brown, J. R. 2001. The role of annuity markets in financing retirement: The MIT Press.
Cheung, S. L. K., Robine, J.-M., Tu, E. J.-C., & Caselli, G. 2005. Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension. Demography, 42(2): 243-258.
Fries, J. F. 2002. Aging, natural death, and the compression of morbidity. BULLETIN-WORLD HEALTH ORGANIZATION, 80(3): 245-250.
Kannisto, V. 2000. Measuring the compression of mortality. Demographic Research, 3(6): 24.
Kannisto, V. 2001. Mode and dispersion of the length of life. Population: An English Selection: 159-171.
Cheung, S., & Robine, J.-M. 2007. Increase in common longevity and the compression of mortality: the case of Japan. Population Studies, 61(1): 85-97.
Li, J. S.-H., Hardy, M. R., & Tan, K. S. 2008. Threshold life tables and their applications. North American Actuarial Journal, 12(2): 99-115.
Lexis, W. 1878. Sur la durée normale de la vie humaine et sur la théorie de la stabilité des rapports statistiques. Annales de Démographie Internationale 2(5): 447-460.
Ouellette, N., & Bourbeau, R. 2011. Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach. Demographic Research, 25(19): 595-628.
Robine, J.-M. 2001. Redefining the stages of the epidemiological transition by a study of the dispersion of life spans: The case of France. Population: An English
Selection: 173-193.
Thatcher, A. R., Cheung, S. L. K., Horiuchi, S., & Robine, J.-M. 2010. The compression of deaths above the mode. Demographic research, 22(17): 505-538.
Willcox, B. J., Donlon, T. A., He, Q., Chen, R., Grove, J. S., Yano, K., Masaki, K. H., Willcox, D. C., Rodriguez, B., & Curb, J. D. 2008. FOXO3A genotype is strongly associated with human longevity. Proceedings of the National Academy of Sciences, 105(37): 13987-13992.
Wilmoth, J. R. 1998. The future of human longevity: a demographer`s perspective. Science, 280(5362): 395-397.
Wilmoth, J. R., & Horiuchi, S. 1999. Rectangularization revisited: Variability of age at death within human populations. Demography, 36(4): 475-495.
Wilmoth, J. R. 2000. Demography of longevity: past, present, and future trends. Experimental gerontology, 35(9): 1111-1129.
Yue, J. C. 2002. Oldest-old mortality rates and the gompertz law: A theoretical and empirical study based on four countries. Journal of Population Studies, 24: 33-57.
Yue, J. C. 2012. Mortality Compression and Longevity Risk. North American Actuarial Journal, 16(4): 434-448.
描述 碩士
國立政治大學
風險管理與保險研究所
100358008
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100358008
資料類型 thesis
dc.contributor.advisor 余清祥zh_TW
dc.contributor.author (Authors) 謝佩文zh_TW
dc.contributor.author (Authors) Hsieh, Pei Wenen_US
dc.creator (作者) 謝佩文zh_TW
dc.creator (作者) Hsieh, Pei Wenen_US
dc.date (日期) 2012en_US
dc.date.accessioned 11-Jul-2013 16:58:17 (UTC+8)-
dc.date.available 11-Jul-2013 16:58:17 (UTC+8)-
dc.date.issued (上傳時間) 11-Jul-2013 16:58:17 (UTC+8)-
dc.identifier (Other Identifiers) G0100358008en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58805-
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) 100358008zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 醫療技術的進步以及生活品質的提升，預計人類平均壽命將持續延長，以臺灣為例，男、女性平均壽命將從2011年的75.98歲、82.65歲，增加到2060年的82.0歲、88.0歲（資料來源：行政院經濟建設委員會2012年推估）。壽命延長意謂更長的退休生活，世界各國在21世紀均面對需求日殷的老年生活照顧，包括退休金制度以及老人醫療等，這些社會福利及保險勢必增加國家財務負擔，因此壽命是否繼續延長或存有極限成為大家關心的議題。近年來，不少研究透過死亡壓縮(Mortality Compression)連結壽命議題，亦即探討死亡年齡是否將集中至更窄的範圍，但因為資料及研究方法的限制，死亡壓縮是否成立仍無定論。
本研究以統計方法、分配假設、資料品質，三個面向來探討死亡壓縮與延壽之間的關係。本研究提出三種數值優化方法：加權最小平方法(Weighted Least Squares；WLS)、非線性極值法(Nonlinear-Maximization；NM)及最大概似估計法(Maximal Likelihood Estimation；MLE)，透過電腦模擬衡量方法優劣，與過去常見的方法比較（Kannisto的SD(M+)），探討何者具有較小的均方誤差(Mean Squared Error；MSE)。其次若死亡年齡之真實死亡分配為t分配時，探討以常態假設代入計算所產生的偏誤；最後則是套入各國實際死亡資料，使用上述較佳的估計方法，檢視死亡壓縮是否存在。
研究結果顯示，NM具有不偏性質且具有較小的均方誤差，過去研究常用的SD(M+)反而有明顯偏誤，且隨著觀察值越多變異數反而增加。而若真實死亡分配若為t分配時，以原先利用常態假設所計算的年金險保費皆有低估的情形，分配的重要性可見一斑，進而探討在實務上常態分配之假設，發現與仍與實際情形有明顯之差異，不論是NM及SD(M+)在死亡壓縮的探討下，皆受到資料的限制而有待商榷。		zh_TW
dc.description.abstract (摘要) Due to the advance in medical technology and the change of life style, the human life expectancy has been increasing since the end of the Second World War II and it is expected to continue the pace of increment. Longer life expectancy also means a longer life after retirement. People living in the 21st century are faced with growing demand for the retirement life, such as the pension funds and medical needs to the individuals, as well as the social welfare and insurance for the elderly to the government. Thus, the issue whether the lifespan has a limit receives a lot of attention. In particular, many studies focus on the topic of mortality compression, which means that the expectancy of lifespan has a limit and variance of lifespan converge. However, due to the availability of elderly data, there is still no consensus if the mortality compression is true.
In this study, we propose estimation methods to estimate modal age and variance of the age-at-death. Three types of methods are involved: weighted least squares (WLS) method, nonlinear maximization (NM) method, and maximum likelihood estimation (MLE) method, and they are compared to the method proposed by Kannisto, namely SD(M+), in 2000. We found that the NM method has a smaller MSE, and we cannot decide the mortality compression is true based on the data from Human Mortality Database. We also applied the normality and t distribution assumption to the age-at-death and compute the pure premiums for annuity products. We found that normality distribution would produce larger premiums than using the empirical mortality rates. Similarity, the bankruptcy probability would be higher if the t distribution is used.		en_US
dc.description.tableofcontents 第壹章、 緒論 1
第一節 研究動機 1
第二節 研究目的 4
第貳章、 文獻探討與方法介紹 6
第一節 存活曲線矩形化 6
第二節 死亡壓縮測量方法 8
第三節 死亡年齡的分配假設－常態壽命區間假設 10
第四節 本研究探究之指標 12
第五節 年金險精算公式及風險值 13
第參章、 數值優化與電腦模擬分析 14
第一節 數值優化之方法 14
第二節 常態壽命區間假設 16
第三節 分配變動對於各種方法之敏感度 19
第肆章、 實證資料分析 24
第一節 資料品質之影響 24
第二節 死亡壓縮與延壽之探討 26
第三節 年金險保費及分配變化之影響 33
第伍章、 殘差檢定 38
第一節 常態檢定－適合度檢定 38
第二節 常態分配假設真實死亡率之差異 40
第陸章、 結論與建議 43
第一節 結論 43
第二節 研究限制 45
參考文獻 46		zh_TW
dc.format.extent 1517431 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100358008en_US
dc.subject (關鍵詞) 死亡壓縮zh_TW
dc.subject (關鍵詞) 生存曲線矩形化zh_TW
dc.subject (關鍵詞) 數值優化zh_TW
dc.subject (關鍵詞) 電腦模擬zh_TW
dc.subject (關鍵詞) 壽險保費zh_TW
dc.subject (關鍵詞) Mortality Compressionen_US
dc.subject (關鍵詞) Rectangularization of Survival Curveen_US
dc.subject (關鍵詞) Optimizationen_US
dc.subject (關鍵詞) Computer Simulationen_US
dc.subject (關鍵詞) Pure Premiumen_US
dc.title (題名) 死亡壓縮與長壽風險之研究zh_TW
dc.title (題名) A Study of Mortality Compression and Longevity Risken_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 中文部分：
王德睦與李大正，2009，台灣的存活曲線矩型化與壽命延長，人口學刊，36：1-31。
李明峰，2012，死亡壓縮與延壽之研究，國立政治大學統計學系碩士論文。

英文部分：
Brown, J. R. 2001. The role of annuity markets in financing retirement: The MIT Press.
Cheung, S. L. K., Robine, J.-M., Tu, E. J.-C., & Caselli, G. 2005. Three dimensions of the survival curve: horizontalization, verticalization, and longevity extension. Demography, 42(2): 243-258.
Fries, J. F. 2002. Aging, natural death, and the compression of morbidity. BULLETIN-WORLD HEALTH ORGANIZATION, 80(3): 245-250.
Kannisto, V. 2000. Measuring the compression of mortality. Demographic Research, 3(6): 24.
Kannisto, V. 2001. Mode and dispersion of the length of life. Population: An English Selection: 159-171.
Cheung, S., & Robine, J.-M. 2007. Increase in common longevity and the compression of mortality: the case of Japan. Population Studies, 61(1): 85-97.
Li, J. S.-H., Hardy, M. R., & Tan, K. S. 2008. Threshold life tables and their applications. North American Actuarial Journal, 12(2): 99-115.
Lexis, W. 1878. Sur la durée normale de la vie humaine et sur la théorie de la stabilité des rapports statistiques. Annales de Démographie Internationale 2(5): 447-460.
Ouellette, N., & Bourbeau, R. 2011. Changes in the age-at-death distribution in four low mortality countries: A nonparametric approach. Demographic Research, 25(19): 595-628.
Robine, J.-M. 2001. Redefining the stages of the epidemiological transition by a study of the dispersion of life spans: The case of France. Population: An English
Selection: 173-193.
Thatcher, A. R., Cheung, S. L. K., Horiuchi, S., & Robine, J.-M. 2010. The compression of deaths above the mode. Demographic research, 22(17): 505-538.
Willcox, B. J., Donlon, T. A., He, Q., Chen, R., Grove, J. S., Yano, K., Masaki, K. H., Willcox, D. C., Rodriguez, B., & Curb, J. D. 2008. FOXO3A genotype is strongly associated with human longevity. Proceedings of the National Academy of Sciences, 105(37): 13987-13992.
Wilmoth, J. R. 1998. The future of human longevity: a demographer`s perspective. Science, 280(5362): 395-397.
Wilmoth, J. R., & Horiuchi, S. 1999. Rectangularization revisited: Variability of age at death within human populations. Demography, 36(4): 475-495.
Wilmoth, J. R. 2000. Demography of longevity: past, present, and future trends. Experimental gerontology, 35(9): 1111-1129.
Yue, J. C. 2002. Oldest-old mortality rates and the gompertz law: A theoretical and empirical study based on four countries. Journal of Population Studies, 24: 33-57.
Yue, J. C. 2012. Mortality Compression and Longevity Risk. North American Actuarial Journal, 16(4): 434-448.		zh_TW