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題名 保險公司因應死亡率風險之避險策略
Hedging strategy against mortality risk for insurance company
作者 莊晉國
Chuang, Chin Kuo
貢獻者 黃泓智<br>楊曉文
莊晉國
Chuang, Chin Kuo
關鍵詞 死亡率風險
Lee Carter model
CIR model
Maximum Entropy principle
Value at risk
Conditional tail expectation
Karush-Kuhn-Tucker
Mortality risk
Lee Carter model
CIR model
Maximum Entropy principle
Value at risk
Conditional tail expectation
Karush-Kuhn-Tucker
日期 2011
上傳時間 30-Oct-2012 11:24:37 (UTC+8)
摘要 本篇論文主要討論在死亡率改善不確定性之下的避險策略。當保險公司負債面的人壽保單是比年金商品來得多的時候，公司會處於死亡率的風險之下。我們假設死亡率和利率都是隨機的情況，部分的死亡率風險可以經由自然避險而消除，而剩下的死亡率風險和利率風險則由零息債券和保單貼現商品來達到最適避險效果。我們考慮mean variance、VaR和CTE當成目標函數時的避險策略，其中在mean variance的最適避險策略可以導出公式解。由數值結果我們可以得知保單貼現的確是死亡率風險的有效避險工具。
This paper proposes hedging strategies to deal with the uncertainty of mortality improvement. When insurance company has more life insurance contracts than annuities in the liability, it will be under the exposure of mortality risk. We assume both mortality and interest rate risk are stochastic. Part of mortality risk is eliminated by natural hedging and the remaining mortality risk and interest rate risk will be optimally hedged by zero coupon bond and life settlement contract. We consider the hedging strategies with objective functions of mean variance, value at risk and conditional tail expectation. The closed-form optimal hedging formula for mean variance assumption is derived, and the numerical result show the life settlement is indeed a effective hedging instrument against mortality risk.
參考文獻 Blake, D., and Burrows, W., 2001. “Survivor Bonds: Helping to Hedge Mortality Risk”, Journal of Risk and Insurance 68: 339-348.
Brockett, P. L., 1991. Information Theoretic Approach to Actuarial Science: A Unification and Extention of Relevant Theory and Applications, Transactions of the Society of Actuaries, 42: 73-115
Cox, J. C., Ingersoll, Jr., J. E., and Ross, S. A., 1985. “A Theory of the Term Structure of Interest Rates”, Econometrica 53: 385-408.
Cox, S. H. and Y. Lin, 2007. Natural Hedging of Life and Annuity Mortality Risks,North American Actuarial Journal, 11(3): 1-15.
Dowd, K., Blake, D., Cairns, A. J. G., and Dawson, P., 2006. “Survivor Swaps”, Journal of Risk & Insurance 73: 1-17.
Hua Chen, Samuel H. Cox and Zhiqiang Yan, 2010. Hedging Longevity Risk in Life Settlements. Working paper.
Johnny Siu-Hang Li, 2010. Pricing longevity risk with the parametric bootstrap: A maximum entropy approach, Insurance: Mathematics and Economics, 47:176-186.
Johnny Siu-Hang Li and Andrew Cheuk-Yin NG.,2011. Canonical valuation of mortality-linked securities, The Journal of Risk and Insurance, Vol. 78, No. 4, 853-884
Kogure., A., and Kurachi, Y., 2010. A Bayesian Approach to Pricing Longevity Risk Based on Risk-Neutral Predictive Distributions, Insurance: Mathematics and Economics, 46:162-172.
Kuhn, H. W.; Tucker, A. W., 1951. "Nonlinear programming". Proceedings of 2nd Berkeley Symposium. Berkeley: University of California press. pp. 481-492.
Kullback, S., and R. A. Leibler, 1951. On Information and Sufficiency, Annals of Mathematical Statistics, 22: 79-86.
Lee, R.D., Carter, L.R., 1992. Modeling and forecasting US mortality. Journal of the
American Statistical Association 87, 659_675.
Pflug, G., 2000. Some Remarks on the Value-at-Risk and the Conditional
Value-at-Risk. S. Uryasev, ed. Probabilistic Constrained Optimization
Methodology and Applications. Kluwer, Dordrecht, The Netherlands, 272–281.
Trindade, A. A., S. Uryasev, A. Shapiro, and G. Zrazhevsky, 2007. Financial
Prediction with Constrained Tail Risk. Journal of Banking and Finance 31 3524–
3538.
Tsai, J.T., J.L. Wang, and L.Y. Tzeng, 2010. On the optimal product mix in life insurance companies using conditional Value at Risk, Insurance: Mathematics and Economics, 46, 235-241.
Wang, J.L., H.C. Huang, S.S. Yang, J.T. Tsai, 2010. An optimal product mix
for hedging longevity risk in life insurance companies: The immunization theory
approach, The Journal of Risk and Insurance, Vol. 77, No. 2, 473-497.
描述 碩士
國立政治大學
風險管理與保險研究所
99358007
100
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099358007
資料類型 thesis
dc.contributor.advisor 黃泓智<br>楊曉文zh_TW
dc.contributor.author (Authors) 莊晉國zh_TW
dc.contributor.author (Authors) Chuang, Chin Kuoen_US
dc.creator (作者) 莊晉國zh_TW
dc.creator (作者) Chuang, Chin Kuoen_US
dc.date (日期) 2011en_US
dc.date.accessioned 30-Oct-2012 11:24:37 (UTC+8)-
dc.date.available 30-Oct-2012 11:24:37 (UTC+8)-
dc.date.issued (上傳時間) 30-Oct-2012 11:24:37 (UTC+8)-
dc.identifier (Other Identifiers) G0099358007en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54597-
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) 99358007zh_TW
dc.description (描述) 100zh_TW
dc.description.abstract (摘要) 本篇論文主要討論在死亡率改善不確定性之下的避險策略。當保險公司負債面的人壽保單是比年金商品來得多的時候，公司會處於死亡率的風險之下。我們假設死亡率和利率都是隨機的情況，部分的死亡率風險可以經由自然避險而消除，而剩下的死亡率風險和利率風險則由零息債券和保單貼現商品來達到最適避險效果。我們考慮mean variance、VaR和CTE當成目標函數時的避險策略，其中在mean variance的最適避險策略可以導出公式解。由數值結果我們可以得知保單貼現的確是死亡率風險的有效避險工具。zh_TW
dc.description.abstract (摘要) This paper proposes hedging strategies to deal with the uncertainty of mortality improvement. When insurance company has more life insurance contracts than annuities in the liability, it will be under the exposure of mortality risk. We assume both mortality and interest rate risk are stochastic. Part of mortality risk is eliminated by natural hedging and the remaining mortality risk and interest rate risk will be optimally hedged by zero coupon bond and life settlement contract. We consider the hedging strategies with objective functions of mean variance, value at risk and conditional tail expectation. The closed-form optimal hedging formula for mean variance assumption is derived, and the numerical result show the life settlement is indeed a effective hedging instrument against mortality risk.en_US
dc.description.tableofcontents ABSTRACT I
CONTENTS II
LIST OF TABLES III
LIST OF FIGURES IV
1.INTRODUCTION 1
2.MODELS SETTING 2
2.1 INTEREST RATE AND MORTALITY RATE MODEL 2
2.2.THE PROFIT FUNCTION 4
2.3.ADJUSTING MORTALITY TABLE 6
3.HEDGING APPROACHES 8
4.NUMERICAL EXAMPLES 11
5.CONCLUSIONS 22
REFERENCE: 24
APPENDIX: 26
1.KARUSH-KUHN-TUCKER (KKT) OPTIMALITY CONDITIONS: 26
2.SOLUTION OF THE OPTIMAL HEDGING PROBLEM 26		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099358007en_US
dc.subject (關鍵詞) 死亡率風險zh_TW
dc.subject (關鍵詞) Lee Carter modelzh_TW
dc.subject (關鍵詞) CIR modelzh_TW
dc.subject (關鍵詞) Maximum Entropy principlezh_TW
dc.subject (關鍵詞) Value at riskzh_TW
dc.subject (關鍵詞) Conditional tail expectationzh_TW
dc.subject (關鍵詞) Karush-Kuhn-Tuckerzh_TW
dc.subject (關鍵詞) Mortality risken_US
dc.subject (關鍵詞) Lee Carter modelen_US
dc.subject (關鍵詞) CIR modelen_US
dc.subject (關鍵詞) Maximum Entropy principleen_US
dc.subject (關鍵詞) Value at risken_US
dc.subject (關鍵詞) Conditional tail expectationen_US
dc.subject (關鍵詞) Karush-Kuhn-Tuckeren_US
dc.title (題名) 保險公司因應死亡率風險之避險策略zh_TW
dc.title (題名) Hedging strategy against mortality risk for insurance companyen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Blake, D., and Burrows, W., 2001. “Survivor Bonds: Helping to Hedge Mortality Risk”, Journal of Risk and Insurance 68: 339-348.
Brockett, P. L., 1991. Information Theoretic Approach to Actuarial Science: A Unification and Extention of Relevant Theory and Applications, Transactions of the Society of Actuaries, 42: 73-115
Cox, J. C., Ingersoll, Jr., J. E., and Ross, S. A., 1985. “A Theory of the Term Structure of Interest Rates”, Econometrica 53: 385-408.
Cox, S. H. and Y. Lin, 2007. Natural Hedging of Life and Annuity Mortality Risks,North American Actuarial Journal, 11(3): 1-15.
Dowd, K., Blake, D., Cairns, A. J. G., and Dawson, P., 2006. “Survivor Swaps”, Journal of Risk & Insurance 73: 1-17.
Hua Chen, Samuel H. Cox and Zhiqiang Yan, 2010. Hedging Longevity Risk in Life Settlements. Working paper.
Johnny Siu-Hang Li, 2010. Pricing longevity risk with the parametric bootstrap: A maximum entropy approach, Insurance: Mathematics and Economics, 47:176-186.
Johnny Siu-Hang Li and Andrew Cheuk-Yin NG.,2011. Canonical valuation of mortality-linked securities, The Journal of Risk and Insurance, Vol. 78, No. 4, 853-884
Kogure., A., and Kurachi, Y., 2010. A Bayesian Approach to Pricing Longevity Risk Based on Risk-Neutral Predictive Distributions, Insurance: Mathematics and Economics, 46:162-172.
Kuhn, H. W.; Tucker, A. W., 1951. "Nonlinear programming". Proceedings of 2nd Berkeley Symposium. Berkeley: University of California press. pp. 481-492.
Kullback, S., and R. A. Leibler, 1951. On Information and Sufficiency, Annals of Mathematical Statistics, 22: 79-86.
Lee, R.D., Carter, L.R., 1992. Modeling and forecasting US mortality. Journal of the
American Statistical Association 87, 659_675.
Pflug, G., 2000. Some Remarks on the Value-at-Risk and the Conditional
Value-at-Risk. S. Uryasev, ed. Probabilistic Constrained Optimization
Methodology and Applications. Kluwer, Dordrecht, The Netherlands, 272–281.
Trindade, A. A., S. Uryasev, A. Shapiro, and G. Zrazhevsky, 2007. Financial
Prediction with Constrained Tail Risk. Journal of Banking and Finance 31 3524–
3538.
Tsai, J.T., J.L. Wang, and L.Y. Tzeng, 2010. On the optimal product mix in life insurance companies using conditional Value at Risk, Insurance: Mathematics and Economics, 46, 235-241.
Wang, J.L., H.C. Huang, S.S. Yang, J.T. Tsai, 2010. An optimal product mix
for hedging longevity risk in life insurance companies: The immunization theory
approach, The Journal of Risk and Insurance, Vol. 77, No. 2, 473-497.		zh_TW