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題名 長壽風險對保單責任準備金之影響-以增額型終身壽險為例
The effect of longevity risk on reserves – based on increasing whole life insurance
作者 陳志岳
貢獻者 蔡政憲
陳志岳
關鍵詞 長壽風險
死亡率模型
增額型終身壽險
保單責任準備金
增額準備金
Lee-Carter Model
RBC制度
longevity risk
increasing whole life insurance policy
Lee-Carter model
risk-based capital (RBC)
日期 2009
上傳時間 8-Dec-2010 16:40:57 (UTC+8)
摘要 近年隨著油價、物價上漲所導致的通貨膨脹風險,壽險業者以增額型終身壽險來吸引潛在消費者。另外,由於醫療技術的進步,使得死亡率逐年改善,因此將造成保單在設計時可能將遭受到長壽風險的影響。本篇文章的主要目的即探討長壽風險對於保單責任準備金的影響,並以增額型終身壽險作為本文主要分析標的。首先建構死亡率模型(Lee-Carter模型),用來配適並模擬死亡率,接著探討增額型終身壽險在各保單年度下之現金流量以及責任準備金的提存,進一步再引進不同的死亡率來探討其現金流量分佈情形與責任準備金之提存。本文研究結果發現,在保險公司未採用遞迴方式計算保費時,當繳費期間愈短、複利利率愈高以及投保年齡愈低時,保險公司所面臨之長壽風險愈大,其後在帶入各種不同死亡率模型,發現死亡改善率愈高,保險公司所面臨之長壽風險愈大,而保險公司在提存責任準備金時,並未考慮到死亡改善率的部分,此對保險公司的財務健全將造成隱憂,本文於此部分建議監理機關透過法規(RBC)的制訂,調整準備金提存的係數,以降低長壽風險對保險公司財務之衝擊。

關鍵字:長壽風險、死亡率模型、增額型終身壽險、保單責任準備金、增額準備金、Lee-Carter Model以及RBC制度。
With the improvement of medical technology, the life expectancy around the world is increasing year by year during the past decade. Therefore, the increasing whole life insurance policy is popular during these years because its benefits are escalating with time and policyholders think they could gain more benefits when they live longer. Like annuity policies, the increasing whole life insurance could also suffer from the longevity risk, which may have enormous impact on the financial statements of insurers.
The purpose of this paper is to discuss the impact of longevity risk on reserves, based on increasing whole life insurance policy. First, we construct Lee-Carter model to fit and simulate mortality rate and assume different mortality improvements from the 2002 Taiwan Standard Ordinary Experience Mortality Table (2002TSO) for further comparisons. And then, we construct a simple model to analyze the cash flows of the increasing whole life policies based on the mortality rates we observed.
By constructing a simple model and simulation, we find that if the insurance company does not correctly estimate longevity risk, the insurance company will lose money on the increasing whole life policies. In order to mitigate the insufficiency of life insurers for the increasing whole life policies, we try to provide some supervision suggestion from the view of the risk-based capital (RBC) requirements. We calculate the factor of insurance risk (C2) of RBC requirements because this factor represents the surplus needed to provide for excess claims over expected, both from random fluctuations and from inaccurate pricing for future levels of claims.

Keywords: longevity risk, increasing whole life insurance policy, Lee-Carter model, risk-based capital (RBC).
參考文獻 余清祥,2002,高高齡老人死亡率與Gompertz模型:理論與實證研究,人口學刊,24,33-58。
李文炯、周世宏,2002,臺灣地區人口死亡率之參數模型,保險專刊,18,28-37。
許鳴遠,2006,台灣人口死亡模型之探討:RF模型的實證研究,政治大學風險管理與保險研究所碩士論文。
陳梅君,2003,考慮死亡率改善下對人壽保險商品費率的影響,淡江大學保險經營研究所碩士論文。
曾奕祥、余清祥,2005,Lee-Carter模型分析:台灣地區死亡率推估之研究,2005年台灣人口學會學術研討會。
楊曉文、梁正德、繆震宇,2009,「長壽風險對壽險業之經營影響及因應策略」,財團法人保險事業發展中心。
Booth, H., J. Maindonald, and L. Smith, 2002. Applying Lee-Carter under Conditions of Variable Mortality Decline. Population Studies 56, 325-336.
Broekhoven, H., 2002. Market Value of Liabilities Mortality Risk: A Practical Model, North American Actuarial Journal 6, 95-106.
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.
Cairns, A.J.G., D. Blake, K. Dowd, G.D. Coughlan, D. Epstein, A. Ong, and I. Balevich, 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.
Carter, L.R. and R.D. Lee, 1992. Modeling and Forecasting U.S. Mortality, Journal of the American Statistical Association 87, 659-675.
CMI committee, 1999. Stochastic Tables of Mortality Based on the 1991-1994 Experience. Continuous Mortality Investigation Report, vol.17. Institute and Faculty of Actuaries, 1-227.
Currie, I.D., 2006. Smoothing and Forecasting Mortality Rates with P-splines. Talk given at the Institute of Actuaries, June 2006.
Gompertz, B., 1825. On the Nature of the Function Expressive of the Law of Human Mortality and on a New Mode of Determining Life Contingencies, Philosophical Transactions of the Royal Society of London 115, 513-585.
Huang, H.C., J.C. Yue, and S.S. Yang, 2008. An Empirical Study of Mortality Models in Taiwan. Asia-Pacific Journal of Risk and Insurance 3, 150-164.
Khalaf-Allah, M., S. Haberman, and R. Verrall, 2006. Measuring the effect of mortality improvements on the cost of annuities. Insurance: Mathematics and Economics 39, 231-249.
Koissi, M.C. and A.F. Shapiro, 2006. Fuzzy Formulation of the Lee-Carter Model for Mortality Forecasting. Insurance: Mathematics and Economics 39, 287-309.
Koissi, M.C., A.F. Shapiro, and G. Hognas, 2006. Evaluating and Extending the Lee-Carter Model for Mortality Forecasting: Bootstrap Confidence Interval. Insurance: Mathematics and Economics 38, 1-20.
Lee, R. and T. Miller, 2001. Evaluating the Performance of the Lee-Carter Method for Forecasting Mortality. Demography 38, 537-549.
Lee, R., 2000. The Lee-Carter Method for Forecasting Mortality with Various Extensions and Applications. North American Actuarial Journal 4, 80-93.
Lewis, E.B., 1982. Control of Body Segment differentiation in Drosophila by the Bithorax Gene Complex, Embryonic Development, Part A: Genetics Aspects, Edited by Burger, M. M. and R. Weber. Alan R. Liss, New York, pp. 269-288.
Makeham, W.M., 1860. On the Law of Mortality and the Construction of Annuity Tables, Journal of the Institute of Actuaries, 13, 325-358.
Natacha B., D. Michel and K.V. Jeroen, 2002. A Poisson Log-Bilinear Regression Approach to the Construction of Projected Lifetables, Insurance: Mathematics and Economics, 31, 373-393.
Olivieri, A., 2001. Uncertainty in mortality projections: An actuarial perspective. Insurance: Mathematics and Economics 29, 231-245.
Olivieri, A., Pitacco, E., 2002. Inference about mortality improvement in life annuity portfolios. In: 27th International Congress of Actuaries, Cancun, Mexico.
Renshaw, A.E. and S. Haberman, 2000. Modelling for Mortality Reduction Factors. Actuarial Research Paper No.127, City University, London.
Renshaw, A.E. and S. Haberman, 2003a. Lee-Carter Mortality Forecasting with Age-specific Enhancement. Insurance: Mathematics and Economics 33, 255-272.
Renshaw, A.E. and S. Haberman, 2003b. On the Forecasting of Mortality Reduction Factors. Insurance: Mathematics and Economics 32, 379-401.
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.
Tzeng, L.Y. and Karen C. Su, 2009, "Longevity Risk in Life Insurance Contract with Escalating Benefits", Working Paper.
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.
Yang, S.S. and H.C. Huang, 2010. Modelling Longevity Risk Using Principle Component. Insurance: Mathematics and Economics 46, 254-270.
描述 碩士
國立政治大學
風險管理與保險研究所
97358016
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097358016
資料類型 thesis
dc.contributor.advisor 蔡政憲zh_TW
dc.contributor.author (Authors) 陳志岳zh_TW
dc.creator (作者) 陳志岳zh_TW
dc.date (日期) 2009en_US
dc.date.accessioned 8-Dec-2010 16:40:57 (UTC+8)-
dc.date.available 8-Dec-2010 16:40:57 (UTC+8)-
dc.date.issued (上傳時間) 8-Dec-2010 16:40:57 (UTC+8)-
dc.identifier (Other Identifiers) G0097358016en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49683-
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) 97358016zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 近年隨著油價、物價上漲所導致的通貨膨脹風險,壽險業者以增額型終身壽險來吸引潛在消費者。另外,由於醫療技術的進步,使得死亡率逐年改善,因此將造成保單在設計時可能將遭受到長壽風險的影響。本篇文章的主要目的即探討長壽風險對於保單責任準備金的影響,並以增額型終身壽險作為本文主要分析標的。首先建構死亡率模型(Lee-Carter模型),用來配適並模擬死亡率,接著探討增額型終身壽險在各保單年度下之現金流量以及責任準備金的提存,進一步再引進不同的死亡率來探討其現金流量分佈情形與責任準備金之提存。本文研究結果發現,在保險公司未採用遞迴方式計算保費時,當繳費期間愈短、複利利率愈高以及投保年齡愈低時,保險公司所面臨之長壽風險愈大,其後在帶入各種不同死亡率模型,發現死亡改善率愈高,保險公司所面臨之長壽風險愈大,而保險公司在提存責任準備金時,並未考慮到死亡改善率的部分,此對保險公司的財務健全將造成隱憂,本文於此部分建議監理機關透過法規(RBC)的制訂,調整準備金提存的係數,以降低長壽風險對保險公司財務之衝擊。

關鍵字:長壽風險、死亡率模型、增額型終身壽險、保單責任準備金、增額準備金、Lee-Carter Model以及RBC制度。
zh_TW
dc.description.abstract (摘要) With the improvement of medical technology, the life expectancy around the world is increasing year by year during the past decade. Therefore, the increasing whole life insurance policy is popular during these years because its benefits are escalating with time and policyholders think they could gain more benefits when they live longer. Like annuity policies, the increasing whole life insurance could also suffer from the longevity risk, which may have enormous impact on the financial statements of insurers.
The purpose of this paper is to discuss the impact of longevity risk on reserves, based on increasing whole life insurance policy. First, we construct Lee-Carter model to fit and simulate mortality rate and assume different mortality improvements from the 2002 Taiwan Standard Ordinary Experience Mortality Table (2002TSO) for further comparisons. And then, we construct a simple model to analyze the cash flows of the increasing whole life policies based on the mortality rates we observed.
By constructing a simple model and simulation, we find that if the insurance company does not correctly estimate longevity risk, the insurance company will lose money on the increasing whole life policies. In order to mitigate the insufficiency of life insurers for the increasing whole life policies, we try to provide some supervision suggestion from the view of the risk-based capital (RBC) requirements. We calculate the factor of insurance risk (C2) of RBC requirements because this factor represents the surplus needed to provide for excess claims over expected, both from random fluctuations and from inaccurate pricing for future levels of claims.

Keywords: longevity risk, increasing whole life insurance policy, Lee-Carter model, risk-based capital (RBC).
en_US
dc.description.tableofcontents 第壹章、研究動機與目的 1
第貳章、文獻回顧 3
第一節、死亡率模型 3
第二節、長壽風險 5
第參章、建構死亡率模型與複利增額型保單現金流量分析 7
第一節、死亡率模型 7
第二節、複利增額型保單之簡介 13
第三節、複利增額型保單之問題--資產額份分析與準備金 14
第四節、保單設計與死亡率模型對資產額份之影響 20
第肆章、保費不足準備金與增額準備金 29
第伍章、C2保險風險值之分析 35
第一節、風險資本額(RBC)制度 35
第二節、C2保險風險係數試算 37
第三節、以遞迴方式計算保費 42
第四節、小結 44
第陸章、結論與建議 45
第一節、結論 45
第二節、建議 46
附錄 47
一、增額型終身壽險保單統計表 47
二、Lee-Carter死亡率模型配適資料 49
三、保險金額 52
四、資產額份分析 53
五、準備金 55
六、台灣RBC之保險風險衡量與係數 68
參考文獻 71

表目錄
表 1 MAPE指標(Lewis, 1982) 9
表 2 參數設定 17
表 3 保單價值準備金 17
表 4 身故之實際保險給付 18
表 5 長壽風險對增額型保單之影響 34
表 6 C2保險風險係數估計 40
表 7 C2保險風險係數估計 43
表 8 C2保險風險係數估計 43

圖目錄
圖 1 以年齡組為間隔的MAPE 9
圖 2 以年代為間隔的MAPE 10
圖 3  之時間趨勢圖 11
圖 4  之時間趨勢圖 11
圖 5 各死亡率模型下之死亡率分布圖 12
圖 6 傳統保單與複利增額保單淨現金流量比較圖 19
圖 7 傳統保單與複利增額保單資產額份比較圖 20
圖 8 複利增額保單在不同投資報酬率下之資產額份圖 20
圖 9 繳費期間對資產額份分布之影響 (35歲投保) 22
圖 10 各死亡改善率下之資產額份 (6年繳費) 23
圖 11 各死亡改善率下之資產額份 (10年繳費) 23
圖 12 各死亡改善率下之資產額份 (20年繳費) 24
圖 13 投保年齡對資產額份分布之影響 (20年繳費) 25
圖 14 各死亡改善率下之資產額份(5歲投保) 25
圖 15 各死亡改善率下之資產額份(65歲投保) 26
圖 16 複利利率對資產額份分布之影響 (35歲投保、20年繳費) 27
圖 17 各死亡改善率下之資產額份(4%,7%) 28
圖 18 各死亡改善率下之資產額份(2%,5%) 28
圖 19 各項準備金 (投保年齡35歲,繳費期間20年) 31
圖 20 各項準備金 (投保年齡35歲,繳費期間20年,利率2.25%) 32
圖 21 不同利率下之增額準備金比較 32
圖 22 各死亡率模型下增額準備金之比較 33
zh_TW
dc.format.extent 848572 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/#G0097358016en_US
dc.subject (關鍵詞) 長壽風險zh_TW
dc.subject (關鍵詞) 死亡率模型zh_TW
dc.subject (關鍵詞) 增額型終身壽險zh_TW
dc.subject (關鍵詞) 保單責任準備金zh_TW
dc.subject (關鍵詞) 增額準備金zh_TW
dc.subject (關鍵詞) Lee-Carter Modelzh_TW
dc.subject (關鍵詞) RBC制度zh_TW
dc.subject (關鍵詞) longevity risken_US
dc.subject (關鍵詞) increasing whole life insurance policyen_US
dc.subject (關鍵詞) Lee-Carter modelen_US
dc.subject (關鍵詞) risk-based capital (RBC)en_US
dc.title (題名) 長壽風險對保單責任準備金之影響-以增額型終身壽險為例zh_TW
dc.title (題名) The effect of longevity risk on reserves – based on increasing whole life insuranceen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 余清祥,2002,高高齡老人死亡率與Gompertz模型:理論與實證研究,人口學刊,24,33-58。zh_TW
dc.relation.reference (參考文獻) 李文炯、周世宏,2002,臺灣地區人口死亡率之參數模型,保險專刊,18,28-37。zh_TW
dc.relation.reference (參考文獻) 許鳴遠,2006,台灣人口死亡模型之探討:RF模型的實證研究,政治大學風險管理與保險研究所碩士論文。zh_TW
dc.relation.reference (參考文獻) 陳梅君,2003,考慮死亡率改善下對人壽保險商品費率的影響,淡江大學保險經營研究所碩士論文。zh_TW
dc.relation.reference (參考文獻) 曾奕祥、余清祥,2005,Lee-Carter模型分析:台灣地區死亡率推估之研究,2005年台灣人口學會學術研討會。zh_TW
dc.relation.reference (參考文獻) 楊曉文、梁正德、繆震宇,2009,「長壽風險對壽險業之經營影響及因應策略」,財團法人保險事業發展中心。zh_TW
dc.relation.reference (參考文獻) Booth, H., J. Maindonald, and L. Smith, 2002. Applying Lee-Carter under Conditions of Variable Mortality Decline. Population Studies 56, 325-336.zh_TW
dc.relation.reference (參考文獻) Broekhoven, H., 2002. Market Value of Liabilities Mortality Risk: A Practical Model, North American Actuarial Journal 6, 95-106.zh_TW
dc.relation.reference (參考文獻) 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) Cairns, A.J.G., D. Blake, K. Dowd, G.D. Coughlan, D. Epstein, A. Ong, and I. Balevich, 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.zh_TW
dc.relation.reference (參考文獻) Carter, L.R. and R.D. Lee, 1992. Modeling and Forecasting U.S. Mortality, Journal of the American Statistical Association 87, 659-675.zh_TW
dc.relation.reference (參考文獻) CMI committee, 1999. Stochastic Tables of Mortality Based on the 1991-1994 Experience. Continuous Mortality Investigation Report, vol.17. Institute and Faculty of Actuaries, 1-227.zh_TW
dc.relation.reference (參考文獻) Currie, I.D., 2006. Smoothing and Forecasting Mortality Rates with P-splines. Talk given at the Institute of Actuaries, June 2006.zh_TW
dc.relation.reference (參考文獻) Gompertz, B., 1825. On the Nature of the Function Expressive of the Law of Human Mortality and on a New Mode of Determining Life Contingencies, Philosophical Transactions of the Royal Society of London 115, 513-585.zh_TW
dc.relation.reference (參考文獻) Huang, H.C., J.C. Yue, and S.S. Yang, 2008. An Empirical Study of Mortality Models in Taiwan. Asia-Pacific Journal of Risk and Insurance 3, 150-164.zh_TW
dc.relation.reference (參考文獻) Khalaf-Allah, M., S. Haberman, and R. Verrall, 2006. Measuring the effect of mortality improvements on the cost of annuities. Insurance: Mathematics and Economics 39, 231-249.zh_TW
dc.relation.reference (參考文獻) Koissi, M.C. and A.F. Shapiro, 2006. Fuzzy Formulation of the Lee-Carter Model for Mortality Forecasting. Insurance: Mathematics and Economics 39, 287-309.zh_TW
dc.relation.reference (參考文獻) Koissi, M.C., A.F. Shapiro, and G. Hognas, 2006. Evaluating and Extending the Lee-Carter Model for Mortality Forecasting: Bootstrap Confidence Interval. Insurance: Mathematics and Economics 38, 1-20.zh_TW
dc.relation.reference (參考文獻) Lee, R. and T. Miller, 2001. Evaluating the Performance of the Lee-Carter Method for Forecasting Mortality. Demography 38, 537-549.zh_TW
dc.relation.reference (參考文獻) Lee, R., 2000. The Lee-Carter Method for Forecasting Mortality with Various Extensions and Applications. North American Actuarial Journal 4, 80-93.zh_TW
dc.relation.reference (參考文獻) Lewis, E.B., 1982. Control of Body Segment differentiation in Drosophila by the Bithorax Gene Complex, Embryonic Development, Part A: Genetics Aspects, Edited by Burger, M. M. and R. Weber. Alan R. Liss, New York, pp. 269-288.zh_TW
dc.relation.reference (參考文獻) Makeham, W.M., 1860. On the Law of Mortality and the Construction of Annuity Tables, Journal of the Institute of Actuaries, 13, 325-358.zh_TW
dc.relation.reference (參考文獻) Natacha B., D. Michel and K.V. Jeroen, 2002. A Poisson Log-Bilinear Regression Approach to the Construction of Projected Lifetables, Insurance: Mathematics and Economics, 31, 373-393.zh_TW
dc.relation.reference (參考文獻) Olivieri, A., 2001. Uncertainty in mortality projections: An actuarial perspective. Insurance: Mathematics and Economics 29, 231-245.zh_TW
dc.relation.reference (參考文獻) Olivieri, A., Pitacco, E., 2002. Inference about mortality improvement in life annuity portfolios. In: 27th International Congress of Actuaries, Cancun, Mexico.zh_TW
dc.relation.reference (參考文獻) Renshaw, A.E. and S. Haberman, 2000. Modelling for Mortality Reduction Factors. Actuarial Research Paper No.127, City University, London.zh_TW
dc.relation.reference (參考文獻) Renshaw, A.E. and S. Haberman, 2003a. Lee-Carter Mortality Forecasting with Age-specific Enhancement. Insurance: Mathematics and Economics 33, 255-272.zh_TW
dc.relation.reference (參考文獻) Renshaw, A.E. and S. Haberman, 2003b. On the Forecasting of Mortality Reduction Factors. Insurance: Mathematics and Economics 32, 379-401.zh_TW
dc.relation.reference (參考文獻) 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) Tzeng, L.Y. and Karen C. Su, 2009, "Longevity Risk in Life Insurance Contract with Escalating Benefits", Working Paper.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Yang, S.S. and H.C. Huang, 2010. Modelling Longevity Risk Using Principle Component. Insurance: Mathematics and Economics 46, 254-270.zh_TW