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題名 高齡死亡模型與年金保險應用之研究
A Study of Elderly Mortality Models and Their Applications in Annuity Insurance作者 陳怡萱
Chen, Yi Xuan貢獻者 余清祥
Yue, C.J.
陳怡萱
Chen, Yi Xuan關鍵詞 長壽風險
高齡死亡模型
死亡改善
電腦模擬
交叉驗證
Longevity Risk
Elderly Mortality Models
Mortality Improvement
Simulation
Cross Validation日期 2013 上傳時間 1-Oct-2014 13:33:54 (UTC+8) 摘要 傳統上國人寄望養兒防老，但面臨少子化及壽命延長，家庭已無法獨力負擔照顧老年人的責任，必須仰賴個人（老年人自己）、國家及政府分擔人口老化造成的需求，這也是政府在過去二十年來積極投入更多資源，制訂與老年人有關的社會保險、福利及政策的原因。像是1995年開辦的全民健康保險提升了全民健康，其中老年人受惠尤多；2005年的勞工退休金條例、2008年的國民年金保險等，則是因應我國國民壽命延長的社會保險制度。對於未來費用的需求估算，需要依賴可靠的死亡率預測，但大多數預測並沒有將死亡率改善列入考量，勢必低估長壽風險的衝擊，影響個人的財務規劃、增加國家負債。 有鑑於此，本文研究常用的死亡率模型，評估哪些適合用於描述高齡死亡率的變化，且能用於計算年金商品的定價。本文考量的模型大致分成兩類：關係模型(Relational Models)及隨機模型(Stochastic Models)，第一類包括常用於高齡的Gompertz、Coale-Kisker模型，以及Discount Sequence模型，第二類則有Lee-Carter及CBD等模型。模型比較的方式以長期預測和短期預測，選用交叉驗證的方式驗證死亡率模型的預測結果與觀察值之間的差異。研究結果顯示Discount Sequence、Lee-Carter、CBD隨機模型較能準確描述台灣、日本與美國等三個國家的死亡率特性；但這三個模型在年金險保費並沒有很明顯的訂價差異。另外，若用於短期預測、長期預測比較，又以Discount Sequence的預測結果優於Lee-Carter模型的預測。
Traditionally in Asia, families played the main role in caring their own elderly (i.e., parents and grand-parents), but the declining fertility rates and longer life expectancy make it difficult for the families to take care of the elderly alone. The elderly themselves and the government need to share the burden caused by the aging population. In fact, most Taiwan’s major social policies in the past 20 years are targeting the elderly, such as National Health Insurance, Labor Pension Act and National Pension Insurance. Their planning and financial solvency rely on reliable mortality models and their projections for the elderly population. However, many mortality models do not take into account the mortality improvements and thus underestimate the cost. In this study, we look for elderly mortality models which can reflect the mortality improvements in recent years and use them to price the annuity products. Two types of mortality models are of interest: relational models and stochastic models. The first group includes the Gompertz model, Coale-Kisker model and Discount Sequence; the other group includes the Lee-Carter and CBD models. We utilize these mortality models to project future mortality rates in Taiwan, Japan and U.S., along with the block bootstrap and ARIMA for projection. The model comparison is based on cross-validation, and both short-term and long-term projections are considered. The results show that the Discount Sequence, Lee-Carter model and CBD model have the best model fits for mortality rates and, for the short-term and long-term forecasts, the Discount Sequence is better than the Lee-Carter model.參考文獻 一、中文部分王信忠、余清祥(2011)，規律折扣數列與高齡死亡率，人口學刊，第43期，37-70。王信忠、金碩、余清祥(2012)，小區域死亡率推估之研究，人口學刊，第45期，121-145。行政院經濟建設委員會(2010)，中華民國2012年至2060年人口推計。余清祥(1997)，修勻：統計在保險上的應用，雙葉書廊。余清祥、郭孟坤(2008)，電腦模擬、隨機方法與人口推估的實證研究，人口學刊，第36期，67-98。謝佩文(2013)，死亡壓縮與長壽風險之研究，碩士論文，政治大學風險管理與保險研究所。二、英文部分Cairns, A.J.G., Blake, D., Dowd, K. (2006a). Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk. ASTIN Bulletin, 36, 79-120.Cairns, A.J.G., Blake, D., Dowd, K. (2006b). A Two-factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration. Journal of Risk and Insurance, 73(4), 678-718.Cairns, A.J.G., Blake, D., Dowd, K. Coughlan, G.D., Epstein, D., Ong, A., and Balevich, I. (2009). A Quantitative Comparison of Stochastic Mortality Models Using Data from England and Wales and the United States. North American Actuarial Journal, 13, 1-35.Chan, W.S., Li, S.H., and Li, J. (2014). The CBD Mortality Indexes: Modeling and Applications. North American Actuarial Journal, 18:1, 38-58.Coale, A.J and Kisker, E.E. (1990). Defects in Data on Old-age Mortality in the United States: New Procedures for Calculating Mortality Schedules and Life Tables at the Highest Ages. Asian and Pacific Population Forum, 4:1-31. Gompertz, B. (1825). On the Nature of the Function Expressive of the Law of HumanMortality and on a New Mode of Determining Life Contingencies, PhilosophicalTransactions of the Royal Society of London, 115: 513-585.Lee, R. and Carter, L. (1992). Modeling and Forecasting U.S. Mortality. Journal of the American Statistical Association, 87, 659-671.Li, J.S.H., Ng, A.C.Y., and Chan, W.S. (2011). Modeling Old-age Mortality Risk for the Populations of Australia and New Zealand: An Extreme Value Approach. Mathematics and Computers in Simulation, 18, 1325-1333.Renshaw, A.E. and Haberman, S. (2003). Lee-Carter Mortality Forecasting with Age-specific Enhancement. Insurance: Mathematics and Economics, 33, 255-272.Willets, R. (1999). Mortality in the next millennium. Paper presented to the Staple InnActuarial Society.Yue, C.J. (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, C.J. (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
101358030
102資料來源 http://thesis.lib.nccu.edu.tw/record/#G0101358030 資料類型 thesis dc.contributor.advisor 余清祥 zh_TW dc.contributor.advisor Yue, C.J. en_US dc.contributor.author (Authors) 陳怡萱 zh_TW dc.contributor.author (Authors) Chen, Yi Xuan en_US dc.creator (作者) 陳怡萱 zh_TW dc.creator (作者) Chen, Yi Xuan en_US dc.date (日期) 2013 en_US dc.date.accessioned 1-Oct-2014 13:33:54 (UTC+8) - dc.date.available 1-Oct-2014 13:33:54 (UTC+8) - dc.date.issued (上傳時間) 1-Oct-2014 13:33:54 (UTC+8) - dc.identifier (Other Identifiers) G0101358030 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/70271 - 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) 101358030 zh_TW dc.description (描述) 102 zh_TW dc.description.abstract (摘要) 傳統上國人寄望養兒防老，但面臨少子化及壽命延長，家庭已無法獨力負擔照顧老年人的責任，必須仰賴個人（老年人自己）、國家及政府分擔人口老化造成的需求，這也是政府在過去二十年來積極投入更多資源，制訂與老年人有關的社會保險、福利及政策的原因。像是1995年開辦的全民健康保險提升了全民健康，其中老年人受惠尤多；2005年的勞工退休金條例、2008年的國民年金保險等，則是因應我國國民壽命延長的社會保險制度。對於未來費用的需求估算，需要依賴可靠的死亡率預測，但大多數預測並沒有將死亡率改善列入考量，勢必低估長壽風險的衝擊，影響個人的財務規劃、增加國家負債。 有鑑於此，本文研究常用的死亡率模型，評估哪些適合用於描述高齡死亡率的變化，且能用於計算年金商品的定價。本文考量的模型大致分成兩類：關係模型(Relational Models)及隨機模型(Stochastic Models)，第一類包括常用於高齡的Gompertz、Coale-Kisker模型，以及Discount Sequence模型，第二類則有Lee-Carter及CBD等模型。模型比較的方式以長期預測和短期預測，選用交叉驗證的方式驗證死亡率模型的預測結果與觀察值之間的差異。研究結果顯示Discount Sequence、Lee-Carter、CBD隨機模型較能準確描述台灣、日本與美國等三個國家的死亡率特性；但這三個模型在年金險保費並沒有很明顯的訂價差異。另外，若用於短期預測、長期預測比較，又以Discount Sequence的預測結果優於Lee-Carter模型的預測。 zh_TW dc.description.abstract (摘要) Traditionally in Asia, families played the main role in caring their own elderly (i.e., parents and grand-parents), but the declining fertility rates and longer life expectancy make it difficult for the families to take care of the elderly alone. The elderly themselves and the government need to share the burden caused by the aging population. In fact, most Taiwan’s major social policies in the past 20 years are targeting the elderly, such as National Health Insurance, Labor Pension Act and National Pension Insurance. Their planning and financial solvency rely on reliable mortality models and their projections for the elderly population. However, many mortality models do not take into account the mortality improvements and thus underestimate the cost. In this study, we look for elderly mortality models which can reflect the mortality improvements in recent years and use them to price the annuity products. Two types of mortality models are of interest: relational models and stochastic models. The first group includes the Gompertz model, Coale-Kisker model and Discount Sequence; the other group includes the Lee-Carter and CBD models. We utilize these mortality models to project future mortality rates in Taiwan, Japan and U.S., along with the block bootstrap and ARIMA for projection. The model comparison is based on cross-validation, and both short-term and long-term projections are considered. The results show that the Discount Sequence, Lee-Carter model and CBD model have the best model fits for mortality rates and, for the short-term and long-term forecasts, the Discount Sequence is better than the Lee-Carter model. 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………………………………………………………3第貳章 文獻探討與死亡率模型介紹……………………5第一節 模型介紹………………………………………………………5第二節 死亡率預測方法…………………………………………11第三節 年金險之精算公式……………………………………11第參章 實證資料分析……………………………………………13第一節 資料來源與模型比較基準………………………13第二節 高齡死亡率模型比較分析………………………15第肆章 預測模型比較……………………………………………30第一節 模型預測方法……………………………………………30第二節 推估年數……………………………………………………31第三節 預測結果……………………………………………………32第伍章 商品應用……………………………………………………37第一節 存活曲線……………………………………………………37第二節 年金商品保費比較…………………………………38第陸章 結論與建議………………………………………………40第一節 研究結論……………………………………………………40第二節 後續研究建議……………………………………………42參考文獻……………………………………………………………………………43附錄一 高齡死亡率模型比較分析……………………45附錄二 預測結果……………………………………………………59附錄三 存活曲線與年金險保費…………………………61 zh_TW dc.format.extent 1147265 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/#G0101358030 en_US dc.subject (關鍵詞) 長壽風險 zh_TW dc.subject (關鍵詞) 高齡死亡模型 zh_TW dc.subject (關鍵詞) 死亡改善 zh_TW dc.subject (關鍵詞) 電腦模擬 zh_TW dc.subject (關鍵詞) 交叉驗證 zh_TW dc.subject (關鍵詞) Longevity Risk en_US dc.subject (關鍵詞) Elderly Mortality Models en_US dc.subject (關鍵詞) Mortality Improvement en_US dc.subject (關鍵詞) Simulation en_US dc.subject (關鍵詞) Cross Validation en_US dc.title (題名) 高齡死亡模型與年金保險應用之研究 zh_TW dc.title (題名) A Study of Elderly Mortality Models and Their Applications in Annuity Insurance en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 一、中文部分王信忠、余清祥(2011)，規律折扣數列與高齡死亡率，人口學刊，第43期，37-70。王信忠、金碩、余清祥(2012)，小區域死亡率推估之研究，人口學刊，第45期，121-145。行政院經濟建設委員會(2010)，中華民國2012年至2060年人口推計。余清祥(1997)，修勻：統計在保險上的應用，雙葉書廊。余清祥、郭孟坤(2008)，電腦模擬、隨機方法與人口推估的實證研究，人口學刊，第36期，67-98。謝佩文(2013)，死亡壓縮與長壽風險之研究，碩士論文，政治大學風險管理與保險研究所。二、英文部分Cairns, A.J.G., Blake, D., Dowd, K. (2006a). Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk. ASTIN Bulletin, 36, 79-120.Cairns, A.J.G., Blake, D., Dowd, K. (2006b). A Two-factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration. Journal of Risk and Insurance, 73(4), 678-718.Cairns, A.J.G., Blake, D., Dowd, K. Coughlan, G.D., Epstein, D., Ong, A., and Balevich, I. (2009). A Quantitative Comparison of Stochastic Mortality Models Using Data from England and Wales and the United States. North American Actuarial Journal, 13, 1-35.Chan, W.S., Li, S.H., and Li, J. (2014). The CBD Mortality Indexes: Modeling and Applications. North American Actuarial Journal, 18:1, 38-58.Coale, A.J and Kisker, E.E. (1990). Defects in Data on Old-age Mortality in the United States: New Procedures for Calculating Mortality Schedules and Life Tables at the Highest Ages. Asian and Pacific Population Forum, 4:1-31. Gompertz, B. (1825). On the Nature of the Function Expressive of the Law of HumanMortality and on a New Mode of Determining Life Contingencies, PhilosophicalTransactions of the Royal Society of London, 115: 513-585.Lee, R. and Carter, L. (1992). Modeling and Forecasting U.S. Mortality. Journal of the American Statistical Association, 87, 659-671.Li, J.S.H., Ng, A.C.Y., and Chan, W.S. (2011). Modeling Old-age Mortality Risk for the Populations of Australia and New Zealand: An Extreme Value Approach. Mathematics and Computers in Simulation, 18, 1325-1333.Renshaw, A.E. and Haberman, S. (2003). Lee-Carter Mortality Forecasting with Age-specific Enhancement. Insurance: Mathematics and Economics, 33, 255-272.Willets, R. (1999). Mortality in the next millennium. Paper presented to the Staple InnActuarial Society.Yue, C.J. (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, C.J. (2012). Mortality Compression and Longevity Risk. North American Actuarial Journal, 16(4), 434-448. zh_TW
