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題名 以多個國家輔助單一國家建構死亡率模型—主成分分析之應用
Construct mortality model for a country with deficient data by multi-countries data —application of principal component analysis
作者 王慧婷
貢獻者 黃泓智
王慧婷
關鍵詞 死亡率模型
主成分分析
Lee-Carter模型
日期 2009
上傳時間 8-Dec-2010 01:57:18 (UTC+8)
摘要 對於人口數不多的國家及地區,因為樣本數較少,死亡率的震盪較大,導致死亡率的估計值較不穩定。為解決此種問題,本研究以其他國家的死亡率資料輔助台灣,建構死亡率模型。首先,以群集分析方式選擇適合輔助台灣的國家,也就是死亡率性質相近之國家,本研究建議以死亡改善率做為主要的考量;其次,以主成分分析的方式分解多個國家死亡率,以負荷做為多個國家的共有係數,分數則是隨著資料和時間改變的變數,在研究結果中,5~6個成分個數即會有不錯的配適和預測效果,以五齡組死亡率配適模型為例,成分個數為6時,男性配適Lee-Carter模型全部國家的平均MAPE為5.40%,主成分分析則為4.13%,下降幅度將近24%,而Lee-Carter模型預測的整體MAPE為14.72%,主成分分析為12.22%,下降幅度約17%,因此主成分分析模型確實有明顯改善Lee-Carter模型。

而和台灣死亡率性質相近的國家,主要選入歐洲國家,像是奧地利、法國、愛爾蘭、挪威和西班牙,除了法國和西班牙人口數分別為六千多萬和四千多萬的國家外,其餘三個國家人口數皆不超過一千萬,這說明人口數多寡或許不是輔助小地區建構死亡率模型的唯一重點,應選取適合的國家作為輔助用途。
參考文獻 英文部分
1. Akaike, H. (1973) “Information theory and an extension of the maximum likelihood principle.” Proc. 2nd International Symposium on Information Theory (Eds. B. N. Petrov and F. Csaki), 267-281, Akademiai Kiado, Budapest.
2. Akaike, H. (1974) “A new look at the statistical model identification.” IEEE Transactions on Automatic Control, AC-19, 716-723.
3. Akaike, H. (1978) “A Bayesian analysis of the minimum AIC procedure.” Ann. Inst. Statist. Math., 30A, 9-14.
4. Akaike, H. (1979) “A Bayesian analysis of the minimum AIC procedure of autoregressive model fitting.” Biometrika, 66, 237-242.
5. Bell, W.R. (1997) “Comparing and Assessing Time Series Methods for Forecasting Age-Specific Fertility and Mortality Rates.” Journal of Official Statistics, 13(3): 279-303.
6. Bozik, J.E. and W.R. Bell (1987) “Forecasting Age Specific Fertility Using Principal Components.” Proceeding of the American Statistical Association, Social Statistics Section, 396-401.
7. Cairns, A. J. G., D. Blake., and K. Dowd (2006) “A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration.” Journal of Risk and Insurance, 73: 687-718.
8. Cairns, A.J.G., D. Blake , K. Dowd, G.D. Coughlan, and M. Khalaf-Allah (2010) “Bayesian Stochastic Mortality Modelling for Two Populations.” Pension Institute Discussion Paper PI-1001.
9. Cairns, A. J.G., D. Blake, K. Dowd, G.D. Coughlan, D. Epstein, Ong, A., and I. Balevich (2007) “A quantitative comparison of stochastic mortality models using data from England and Wales and the United States.” Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences.
10. Continuous Mortality Investigation Report No.17 (1999) Institute of Actuaries and Faculty of Actuaries.
11. Currie, I.D. (2006) “Smoothing and Forecasting Mortality Rates with P-Splines.” Paper given at the Institute of Actuaries, June 2006. http://www.ma.hw.ac.uk/~iain/research/talks.html
12. Currie, I.D., M. Durban, and P.H.C. Eilers (2004) “Smoothing and Forecasting Mortality Rates.” Statistical Model, 4: 279-98.
13. Dowd, K., A.J.G. Cairns, D. Blake, G.D. Coughlan, D. Epstein, and M. Khalaf-Allah (2008a) “Backtesting Stochastic Mortality Models: An Ex-Post Evaluation of Multi-Period-Ahead Density Forecasts.” Working Paper.
14. Dowd, K., A.J.G. Cairns, D. Blake, G.D. Coughlan, D. Epstein, and M. Khalaf-Allah (2008b) “Evaluating the Goodness of Fit of Stochastic Mortality Models.” Working Paper.
15. Jarner, S.F., and E.M. Kryger (2009) “Modelling adult mortality in small populations: The SAINT model.” Pension Institute Discussion Paper PI-0902.
16. Lee, R.D., and L.R. Carter (1992) “Modeling and forecasting U.S. mortality”, Journal of the American Statistical Association, 87: 659-765.
17. Lewis, C.D. (1982) “Industrial and business forecasting methods : a practical guide to exponential smoothing and curve fitting.” London: Butterworth Scientific, 1982.
18. Li, N., and R. Lee (2005) “Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method.” Demography, 42(3): 575-594.
19. Mitra, S., and M.L. Levin (1997) “Model the reciprocal of the survivorship function.” Mathematical and Computer Modelling. 26(6): 57-68.
20. Njenga, C.N., and M. Sherris (2009) “Longevity Risk and the Econometric Analysis of Mortality Trends and Volatility.” Working Paper. http://ssrn.com/abstract=1458084 .
21. Pedroza, C. (2006) “A Bayesian forecasting model: predicting U.S. male mortality.” Biostatistics, 7(4): 530-550.
22. Reichmuth, W. and S. Sarferaz (2008) “Bayesian demographic modeling and forecasting: An application to US mortality.” SFB 649 Discussion paper 2008-052.
23. Renshaw, A.E., and S. Haberman (2006) “A cohort-based extension to the Lee-Carter model for mortality reduction factors”, Insurance: Mathematics and Economics, 38: 556-570.
24. Schwartz, G. (1978) “Estimating the dimension of a model.” Ann. Statist., 6, 461-464.
25. Wei, William W. S. (1990) Time Series Analysis: Univariate and Multivariate Methods. (2nd ed.). Redwood City, CA: Addison-Wesley.
26. Yang, Sharon S., Jack C. Yue, Hong-Chih Huang (2010) “Modeling Longevity Risks using a Principal Component Approach: A Comparison with Existing Stochastic Mortality Models”, Insurance: Mathematics and Economics, 46: 254-270.
中文部分
1. 余清祥(1999)。修勻:統計在保險的應用。台北:雙葉書局。
2. 余清祥、曾奕翔(民94年3月)。Lee-Carter模型分析:台灣地區死亡率推估之研究。楊文山(主持人),二十一世紀的臺灣人口發展:趨勢與挑戰。2005年台灣人口學會學術研討會,國立台灣大學。
3. 陳順宇(2005)。多變量分析。四版。台北:華泰書局。
4. 陳文琴(民97)。死亡率改善模型的探討及保險商品自然避險策略之應用。國立政治大學風險管理與保險系研究所碩士論文。台北市。
描述 碩士
國立政治大學
風險管理與保險研究所
97358010
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097358010
資料類型 thesis
dc.contributor.advisor 黃泓智zh_TW
dc.contributor.author (Authors) 王慧婷zh_TW
dc.creator (作者) 王慧婷zh_TW
dc.date (日期) 2009en_US
dc.date.accessioned 8-Dec-2010 01:57:18 (UTC+8)-
dc.date.available 8-Dec-2010 01:57:18 (UTC+8)-
dc.date.issued (上傳時間) 8-Dec-2010 01:57:18 (UTC+8)-
dc.identifier (Other Identifiers) G0097358010en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49032-
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) 97358010zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 對於人口數不多的國家及地區,因為樣本數較少,死亡率的震盪較大,導致死亡率的估計值較不穩定。為解決此種問題,本研究以其他國家的死亡率資料輔助台灣,建構死亡率模型。首先,以群集分析方式選擇適合輔助台灣的國家,也就是死亡率性質相近之國家,本研究建議以死亡改善率做為主要的考量;其次,以主成分分析的方式分解多個國家死亡率,以負荷做為多個國家的共有係數,分數則是隨著資料和時間改變的變數,在研究結果中,5~6個成分個數即會有不錯的配適和預測效果,以五齡組死亡率配適模型為例,成分個數為6時,男性配適Lee-Carter模型全部國家的平均MAPE為5.40%,主成分分析則為4.13%,下降幅度將近24%,而Lee-Carter模型預測的整體MAPE為14.72%,主成分分析為12.22%,下降幅度約17%,因此主成分分析模型確實有明顯改善Lee-Carter模型。

而和台灣死亡率性質相近的國家,主要選入歐洲國家,像是奧地利、法國、愛爾蘭、挪威和西班牙,除了法國和西班牙人口數分別為六千多萬和四千多萬的國家外,其餘三個國家人口數皆不超過一千萬,這說明人口數多寡或許不是輔助小地區建構死亡率模型的唯一重點,應選取適合的國家作為輔助用途。
zh_TW
dc.description.tableofcontents 目次 I
圖次 III
表次 VI
第一章 緒論 1
第一節 研究問題與背景 1
第二節 研究目的 1
第三節 研究架構 2
第二章 文獻探討 3
第一節 死亡率模型 3
第二節 多資料的死亡率模型 8
第三章 研究方法 11
第一節 以群集分析選取國家 11
第二節 以因素分析—主成分法分解死亡率 18
第三節 模型比較標準 23
第四章 研究結果 25
第一節 單齡組死亡率(HMD資料) 26
第二節 五齡組死亡率(HMD資料) 37
第三節 五齡組死亡率模型之改良(HMD資料) 43
第四節 台灣壽險經驗資料 52
第五章 實證應用:保險商品的純保費比較 58
第一節 終身壽險保險費的比較 59
第二節 年金險保險費的比較 60
第六章 結論與建議 61
第一節 選取死亡率性質相近的國家 61
第二節 死亡率模型之配適與預測 61
第三節 實證應用結果 62
參考文獻 63
附錄一:各國死亡改善率圖 66
附錄二:分數趨勢圖 70
一、 七國單齡組分數趨勢圖(HMD資料) 70
二、 五國家五齡組分數趨勢圖(HMD資料) 73
三、 取對數後六國家五齡組分數趨勢圖(HMD資料) 76
四、 台灣壽險經驗資料他國分數趨勢圖 79
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097358010en_US
dc.subject (關鍵詞) 死亡率模型zh_TW
dc.subject (關鍵詞) 主成分分析zh_TW
dc.subject (關鍵詞) Lee-Carter模型zh_TW
dc.title (題名) 以多個國家輔助單一國家建構死亡率模型—主成分分析之應用zh_TW
dc.title (題名) Construct mortality model for a country with deficient data by multi-countries data —application of principal component analysisen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 英文部分zh_TW
dc.relation.reference (參考文獻) 1. Akaike, H. (1973) “Information theory and an extension of the maximum likelihood principle.” Proc. 2nd International Symposium on Information Theory (Eds. B. N. Petrov and F. Csaki), 267-281, Akademiai Kiado, Budapest.zh_TW
dc.relation.reference (參考文獻) 2. Akaike, H. (1974) “A new look at the statistical model identification.” IEEE Transactions on Automatic Control, AC-19, 716-723.zh_TW
dc.relation.reference (參考文獻) 3. Akaike, H. (1978) “A Bayesian analysis of the minimum AIC procedure.” Ann. Inst. Statist. Math., 30A, 9-14.zh_TW
dc.relation.reference (參考文獻) 4. Akaike, H. (1979) “A Bayesian analysis of the minimum AIC procedure of autoregressive model fitting.” Biometrika, 66, 237-242.zh_TW
dc.relation.reference (參考文獻) 5. Bell, W.R. (1997) “Comparing and Assessing Time Series Methods for Forecasting Age-Specific Fertility and Mortality Rates.” Journal of Official Statistics, 13(3): 279-303.zh_TW
dc.relation.reference (參考文獻) 6. Bozik, J.E. and W.R. Bell (1987) “Forecasting Age Specific Fertility Using Principal Components.” Proceeding of the American Statistical Association, Social Statistics Section, 396-401.zh_TW
dc.relation.reference (參考文獻) 7. Cairns, A. J. G., D. Blake., and K. Dowd (2006) “A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration.” Journal of Risk and Insurance, 73: 687-718.zh_TW
dc.relation.reference (參考文獻) 8. Cairns, A.J.G., D. Blake , K. Dowd, G.D. Coughlan, and M. Khalaf-Allah (2010) “Bayesian Stochastic Mortality Modelling for Two Populations.” Pension Institute Discussion Paper PI-1001.zh_TW
dc.relation.reference (參考文獻) 9. Cairns, A. J.G., D. Blake, K. Dowd, G.D. Coughlan, D. Epstein, Ong, A., and I. Balevich (2007) “A quantitative comparison of stochastic mortality models using data from England and Wales and the United States.” Department of Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences.zh_TW
dc.relation.reference (參考文獻) 10. Continuous Mortality Investigation Report No.17 (1999) Institute of Actuaries and Faculty of Actuaries.zh_TW
dc.relation.reference (參考文獻) 11. Currie, I.D. (2006) “Smoothing and Forecasting Mortality Rates with P-Splines.” Paper given at the Institute of Actuaries, June 2006. http://www.ma.hw.ac.uk/~iain/research/talks.htmlzh_TW
dc.relation.reference (參考文獻) 12. Currie, I.D., M. Durban, and P.H.C. Eilers (2004) “Smoothing and Forecasting Mortality Rates.” Statistical Model, 4: 279-98.zh_TW
dc.relation.reference (參考文獻) 13. Dowd, K., A.J.G. Cairns, D. Blake, G.D. Coughlan, D. Epstein, and M. Khalaf-Allah (2008a) “Backtesting Stochastic Mortality Models: An Ex-Post Evaluation of Multi-Period-Ahead Density Forecasts.” Working Paper.zh_TW
dc.relation.reference (參考文獻) 14. Dowd, K., A.J.G. Cairns, D. Blake, G.D. Coughlan, D. Epstein, and M. Khalaf-Allah (2008b) “Evaluating the Goodness of Fit of Stochastic Mortality Models.” Working Paper.zh_TW
dc.relation.reference (參考文獻) 15. Jarner, S.F., and E.M. Kryger (2009) “Modelling adult mortality in small populations: The SAINT model.” Pension Institute Discussion Paper PI-0902.zh_TW
dc.relation.reference (參考文獻) 16. Lee, R.D., and L.R. Carter (1992) “Modeling and forecasting U.S. mortality”, Journal of the American Statistical Association, 87: 659-765.zh_TW
dc.relation.reference (參考文獻) 17. Lewis, C.D. (1982) “Industrial and business forecasting methods : a practical guide to exponential smoothing and curve fitting.” London: Butterworth Scientific, 1982.zh_TW
dc.relation.reference (參考文獻) 18. Li, N., and R. Lee (2005) “Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method.” Demography, 42(3): 575-594.zh_TW
dc.relation.reference (參考文獻) 19. Mitra, S., and M.L. Levin (1997) “Model the reciprocal of the survivorship function.” Mathematical and Computer Modelling. 26(6): 57-68.zh_TW
dc.relation.reference (參考文獻) 20. Njenga, C.N., and M. Sherris (2009) “Longevity Risk and the Econometric Analysis of Mortality Trends and Volatility.” Working Paper. http://ssrn.com/abstract=1458084 .zh_TW
dc.relation.reference (參考文獻) 21. Pedroza, C. (2006) “A Bayesian forecasting model: predicting U.S. male mortality.” Biostatistics, 7(4): 530-550.zh_TW
dc.relation.reference (參考文獻) 22. Reichmuth, W. and S. Sarferaz (2008) “Bayesian demographic modeling and forecasting: An application to US mortality.” SFB 649 Discussion paper 2008-052.zh_TW
dc.relation.reference (參考文獻) 23. Renshaw, A.E., and S. Haberman (2006) “A cohort-based extension to the Lee-Carter model for mortality reduction factors”, Insurance: Mathematics and Economics, 38: 556-570.zh_TW
dc.relation.reference (參考文獻) 24. Schwartz, G. (1978) “Estimating the dimension of a model.” Ann. Statist., 6, 461-464.zh_TW
dc.relation.reference (參考文獻) 25. Wei, William W. S. (1990) Time Series Analysis: Univariate and Multivariate Methods. (2nd ed.). Redwood City, CA: Addison-Wesley.zh_TW
dc.relation.reference (參考文獻) 26. Yang, Sharon S., Jack C. Yue, Hong-Chih Huang (2010) “Modeling Longevity Risks using a Principal Component Approach: A Comparison with Existing Stochastic Mortality Models”, Insurance: Mathematics and Economics, 46: 254-270.zh_TW
dc.relation.reference (參考文獻) 中文部分zh_TW
dc.relation.reference (參考文獻) 1. 余清祥(1999)。修勻:統計在保險的應用。台北:雙葉書局。zh_TW
dc.relation.reference (參考文獻) 2. 余清祥、曾奕翔(民94年3月)。Lee-Carter模型分析:台灣地區死亡率推估之研究。楊文山(主持人),二十一世紀的臺灣人口發展:趨勢與挑戰。2005年台灣人口學會學術研討會,國立台灣大學。zh_TW
dc.relation.reference (參考文獻) 3. 陳順宇(2005)。多變量分析。四版。台北:華泰書局。zh_TW
dc.relation.reference (參考文獻) 4. 陳文琴(民97)。死亡率改善模型的探討及保險商品自然避險策略之應用。國立政治大學風險管理與保險系研究所碩士論文。台北市。zh_TW