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題名 利用共同因子建立多重群體死亡率模型
Using Principal Component Analysis to Construct Multi-Group Mortality Model作者 鄭惠恒
Cheng, Hui Heng貢獻者 王儷玲<br>蔡政憲
Wang, Li Ling<br>Tsai, Cheng Hsien
鄭惠恒
Cheng, Hui Heng關鍵詞 死亡率改善
Lee-Carter 死亡率模型
主成分分析法
共同因子與群體死亡率預測
Mortality Improvement
Lee-Carter Model
Principal Component Analysis
Common Factor Mortality Forecasting
Multi-Group Life Expediency日期 2013 上傳時間 6-Aug-2014 11:41:52 (UTC+8) 摘要 對於商業保險公司和政府單位而言，死亡率的改善和未來死亡率的預估一直是一大重要議題。特別是對於退休金相關的社會保險、勞退或是商業年金、壽險等等，如何找尋一個準確的預估模式對未來的死亡率改善情況進行預測，並釐訂合理的保費及提列適當的準備金，是對於一個保險制度能否永續經營的重要因素。過去所使用的配適方法，大多僅以單一群體的過去資料輔助未來的預測，例如 Li and Carter (1992)所提出的 Lee-Carter Model，或是 Bell (1997)使用主成分分析法 (Principal Component Analysis, PCA)等僅針對單一群體本身變數進行分析之方式。然而綜觀全球死亡率改善趨勢，可發現國與國間、組與祖間雖有不同，但仍具備共同的趨勢。因此在考慮未來的死亡率配適方面，應加入組與組間的共同因子 (common factors) 進行考量。 Li and Lee (2005)曾提出 Augmented Lee-Carter Model，即對原本的Lee-Carter Model進行修正，加入共同因素項，並且得到更好的預測效果。本文則採用考慮共同因子之主成分分析原理建構多重群體死亡率模型，即透過主成分分析法，同時考慮不同群體間的死亡率，並以台灣男性和女性1970年至2010年的死亡率資料，做為兩個子群體進行分析。本文使用之主成分分析法模式，和 Lee-Carter Model (Li and Carter, 1992) 和 Augmented Lee-Carter Model (Li and Lee, 2005)，以MAPE法對個別的預測能力進行分析，並得出採用PCA的模式，在預測男性短年期(5年)內的預估能力屬精確(MAPE 介於10%~20%之間)，然而在長期預估下容易失準，且所有使用的模型，在配適台灣資料時皆發生無法準確預估嬰幼兒期(0~3歲)和老年期(80歲以上)之情形。本文並以所有模型預估之死亡率計算保險公司之準備金與保費提列，並與第五回經驗生命表進行比較。
For governments and life insurance companies, mortality rates are one of the key factors in determining premiums and reserves. Ignoring or miscalculating mortality rates might have negative influences in pricing. However, most of the mortality models do not consider the common trends between groups.In this article, we try to construct the mortality structure which considering common trends of multi-groups populations with principal component analysis (PCA) method. We choose 9 factors to set up our model and fit with the actual data in Taiwan’s gender mortality. We also compare the Lee-Carter Model (Lee and Carter, 1992) and the augmented Lee-Carter Model (Li and Hardy, 2012) with our common factors PCA model, and we find that the PCA model has the least MAPE than other model in five years forecasting in both genders.After finishing basic analysis, we use the mortality data of Taiwan (1970 to 2010) from human mortality database to construct the life expectancy model. We adopt the same criteria to choose the components we need. We also compare the level premium and reserves by different forecasting mortality rates. All of the models indicate life insurance companies to provide higher reserves and level premium than using the 5th TSO experience mortality rare. We will do following research by using company-specific data to construct unique life expectancy model.參考文獻 1 BELL, William R. Comparing and assessing time series methods for forecasting age-specific fertility and mortality rates. JOURNAL OF OFFICIAL STATISTICS-STOCKHOLM-, 1997, 13: 279-304.2 Cairns, A. J. G., D. Blake, and K. Dowd, 2006a, A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration, Journal of Risk and Insurance, 73: 687-718.3 Dahl, M., 2004, Stochastic Mortality in Life Insurance: Market Reserves and Mortality-linked Insurance Contracts, Insurance: Mathematics and Economics, 35: 113-136.4 Dahl, M., and T. Møller, 2005, Valuation and Hedging of Life Insurance Liabilities with Systematic Mortality Risk, In the Proceedings of the 2005 International AFIR Colloquium, Zurich, Available online at http://www.afir2005.ch.5 Hyndman, R. J. and S. Ullah, 2007, Robust Forecasting of Mortality and Fertility Rates: A Functional Data Approach, Computational Statistics and Data Analysis, 51, 4942-4956.6 JARNER, Søren Fiig; KRYGER, Esben Masotti. Modelling adult mortality in small populations: The SAINT model. Astin Bulletin, 2011, 41.02: 377-418.7 RENSHAW, Arthur E.; HABERMAN, Steven. A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 2006, 38.3: 556-570.8 Stallard, E., 2006, Demographic Issues in Longevity Risk Analysis, Journal of Risk and Insurance, 73: 575-609.9 LI, Nan; LEE, Ronald. Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 2005, 42.3: 575-594.10 Lee, R. D. and L. R. Carter, 1992, Modeling and Forecasting U.S. Mortality, Journal of the American Statistical Association, 87: 659-675.11 Lee, R. D. and T. Miller, 2001, Evaluating the Performance of the Lee-Carter Mortality Forecasts, Demography, 38: 537-549.12 Li, J. S. H., & Hardy, M. R, 2011, Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177-200.13 LEWIS, Colin David. Industrial and business forecasting methods: A practical guide to exponential smoothing and curve fitting. London: Butterworth Scientific, 1982.14 McNown, R. and A. Rogers, 1989, Forecasting Mortality: A Parameterized Time Series Approach, Demography, 26: 645-66015 Plat, R., 2009, On Stochastic Mortality Modeling, Insurance: Mathematics and Economics, 45, 393-404.16 Murray, C. J. L., B. D. Ferguson, A. D. Lopez, M. Guillot, J. A. Salomon, and O. Ahmad, 2003, Modified Logit Life Table System: Principles, Empirical Validation, and Application, Population Studies, 57: 165-182.17 SHERRIS, Michael; NJENGA, Carolyn. Longevity Risk and the Econometric Analysis of Mortality Trends and Volatility. UNSW Australian School of Business Research Paper, 2009, 2009ACTL08.18 YANG, Sharon S.; YUE, Jack C.; HUANG, Hong-Chih. Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models. Insurance: Mathematics and Economics, 2010, 46.1: 254-270.19 Yue, C. S. J., & Huang, H. C., 2011. A Study of Incidence Experience for Taiwan Life Insurance. The Geneva Papers on Risk and Insurance-Issues and Practice, 36(4), 718-733. 描述 碩士
國立政治大學
風險管理與保險研究所
101358002
102資料來源 http://thesis.lib.nccu.edu.tw/record/#G0101358002 資料類型 thesis dc.contributor.advisor 王儷玲<br>蔡政憲 zh_TW dc.contributor.advisor Wang, Li Ling<br>Tsai, Cheng Hsien en_US dc.contributor.author (Authors) 鄭惠恒 zh_TW dc.contributor.author (Authors) Cheng, Hui Heng en_US dc.creator (作者) 鄭惠恒 zh_TW dc.creator (作者) Cheng, Hui Heng en_US dc.date (日期) 2013 en_US dc.date.accessioned 6-Aug-2014 11:41:52 (UTC+8) - dc.date.available 6-Aug-2014 11:41:52 (UTC+8) - dc.date.issued (上傳時間) 6-Aug-2014 11:41:52 (UTC+8) - dc.identifier (Other Identifiers) G0101358002 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/68238 - 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) 101358002 zh_TW dc.description (描述) 102 zh_TW dc.description.abstract (摘要) 對於商業保險公司和政府單位而言，死亡率的改善和未來死亡率的預估一直是一大重要議題。特別是對於退休金相關的社會保險、勞退或是商業年金、壽險等等，如何找尋一個準確的預估模式對未來的死亡率改善情況進行預測，並釐訂合理的保費及提列適當的準備金，是對於一個保險制度能否永續經營的重要因素。過去所使用的配適方法，大多僅以單一群體的過去資料輔助未來的預測，例如 Li and Carter (1992)所提出的 Lee-Carter Model，或是 Bell (1997)使用主成分分析法 (Principal Component Analysis, PCA)等僅針對單一群體本身變數進行分析之方式。然而綜觀全球死亡率改善趨勢，可發現國與國間、組與祖間雖有不同，但仍具備共同的趨勢。因此在考慮未來的死亡率配適方面，應加入組與組間的共同因子 (common factors) 進行考量。 Li and Lee (2005)曾提出 Augmented Lee-Carter Model，即對原本的Lee-Carter Model進行修正，加入共同因素項，並且得到更好的預測效果。本文則採用考慮共同因子之主成分分析原理建構多重群體死亡率模型，即透過主成分分析法，同時考慮不同群體間的死亡率，並以台灣男性和女性1970年至2010年的死亡率資料，做為兩個子群體進行分析。本文使用之主成分分析法模式，和 Lee-Carter Model (Li and Carter, 1992) 和 Augmented Lee-Carter Model (Li and Lee, 2005)，以MAPE法對個別的預測能力進行分析，並得出採用PCA的模式，在預測男性短年期(5年)內的預估能力屬精確(MAPE 介於10%~20%之間)，然而在長期預估下容易失準，且所有使用的模型，在配適台灣資料時皆發生無法準確預估嬰幼兒期(0~3歲)和老年期(80歲以上)之情形。本文並以所有模型預估之死亡率計算保險公司之準備金與保費提列，並與第五回經驗生命表進行比較。 zh_TW dc.description.abstract (摘要) For governments and life insurance companies, mortality rates are one of the key factors in determining premiums and reserves. Ignoring or miscalculating mortality rates might have negative influences in pricing. However, most of the mortality models do not consider the common trends between groups.In this article, we try to construct the mortality structure which considering common trends of multi-groups populations with principal component analysis (PCA) method. We choose 9 factors to set up our model and fit with the actual data in Taiwan’s gender mortality. We also compare the Lee-Carter Model (Lee and Carter, 1992) and the augmented Lee-Carter Model (Li and Hardy, 2012) with our common factors PCA model, and we find that the PCA model has the least MAPE than other model in five years forecasting in both genders.After finishing basic analysis, we use the mortality data of Taiwan (1970 to 2010) from human mortality database to construct the life expectancy model. We adopt the same criteria to choose the components we need. We also compare the level premium and reserves by different forecasting mortality rates. All of the models indicate life insurance companies to provide higher reserves and level premium than using the 5th TSO experience mortality rare. We will do following research by using company-specific data to construct unique life expectancy model. en_US dc.description.tableofcontents Abstract iTable of Contents iiList of Figures iiiList of Tables ivIntroduction 1Literature Reviews and Methodology 4Fitting and Forecasting Results 8Conclusions and Suggestions 20References 22 zh_TW dc.format.extent 1098288 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/#G0101358002 en_US dc.subject (關鍵詞) 死亡率改善 zh_TW dc.subject (關鍵詞) Lee-Carter 死亡率模型 zh_TW dc.subject (關鍵詞) 主成分分析法 zh_TW dc.subject (關鍵詞) 共同因子與群體死亡率預測 zh_TW dc.subject (關鍵詞) Mortality Improvement en_US dc.subject (關鍵詞) Lee-Carter Model en_US dc.subject (關鍵詞) Principal Component Analysis en_US dc.subject (關鍵詞) Common Factor Mortality Forecasting en_US dc.subject (關鍵詞) Multi-Group Life Expediency en_US dc.title (題名) 利用共同因子建立多重群體死亡率模型 zh_TW dc.title (題名) Using Principal Component Analysis to Construct Multi-Group Mortality Model en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 1 BELL, William R. Comparing and assessing time series methods for forecasting age-specific fertility and mortality rates. JOURNAL OF OFFICIAL STATISTICS-STOCKHOLM-, 1997, 13: 279-304.2 Cairns, A. J. G., D. Blake, and K. Dowd, 2006a, A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration, Journal of Risk and Insurance, 73: 687-718.3 Dahl, M., 2004, Stochastic Mortality in Life Insurance: Market Reserves and Mortality-linked Insurance Contracts, Insurance: Mathematics and Economics, 35: 113-136.4 Dahl, M., and T. Møller, 2005, Valuation and Hedging of Life Insurance Liabilities with Systematic Mortality Risk, In the Proceedings of the 2005 International AFIR Colloquium, Zurich, Available online at http://www.afir2005.ch.5 Hyndman, R. J. and S. Ullah, 2007, Robust Forecasting of Mortality and Fertility Rates: A Functional Data Approach, Computational Statistics and Data Analysis, 51, 4942-4956.6 JARNER, Søren Fiig; KRYGER, Esben Masotti. Modelling adult mortality in small populations: The SAINT model. Astin Bulletin, 2011, 41.02: 377-418.7 RENSHAW, Arthur E.; HABERMAN, Steven. A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 2006, 38.3: 556-570.8 Stallard, E., 2006, Demographic Issues in Longevity Risk Analysis, Journal of Risk and Insurance, 73: 575-609.9 LI, Nan; LEE, Ronald. Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 2005, 42.3: 575-594.10 Lee, R. D. and L. R. Carter, 1992, Modeling and Forecasting U.S. Mortality, Journal of the American Statistical Association, 87: 659-675.11 Lee, R. D. and T. Miller, 2001, Evaluating the Performance of the Lee-Carter Mortality Forecasts, Demography, 38: 537-549.12 Li, J. S. H., & Hardy, M. R, 2011, Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177-200.13 LEWIS, Colin David. Industrial and business forecasting methods: A practical guide to exponential smoothing and curve fitting. London: Butterworth Scientific, 1982.14 McNown, R. and A. Rogers, 1989, Forecasting Mortality: A Parameterized Time Series Approach, Demography, 26: 645-66015 Plat, R., 2009, On Stochastic Mortality Modeling, Insurance: Mathematics and Economics, 45, 393-404.16 Murray, C. J. L., B. D. Ferguson, A. D. Lopez, M. Guillot, J. A. Salomon, and O. Ahmad, 2003, Modified Logit Life Table System: Principles, Empirical Validation, and Application, Population Studies, 57: 165-182.17 SHERRIS, Michael; NJENGA, Carolyn. Longevity Risk and the Econometric Analysis of Mortality Trends and Volatility. UNSW Australian School of Business Research Paper, 2009, 2009ACTL08.18 YANG, Sharon S.; YUE, Jack C.; HUANG, Hong-Chih. Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models. Insurance: Mathematics and Economics, 2010, 46.1: 254-270.19 Yue, C. S. J., & Huang, H. C., 2011. A Study of Incidence Experience for Taiwan Life Insurance. The Geneva Papers on Risk and Insurance-Issues and Practice, 36(4), 718-733. zh_TW
