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題名：死亡率模型:長壽風險管理之應用
作者：林子綾 引用關係
作者(外文)：Tzu-Ling Lin
校院名稱：國立臺灣大學
系所名稱：財務金融學研究所
指導教授：曾郁仁
學位類別：博士
出版日期：2010
主題關鍵詞：隨機死亡率；波動率；長壽風險；死亡率風險；年金；stochastic mortality；volatilities；longevity risk；mortality risk；annuity
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本論文包含兩篇重點在死亡率模型與長壽風險應用之文章。第一篇提出用相加結構改進Ballotta and Haberman (2006)的模型，因為我們認為B&H 的模型會有兩個值得質疑的特性。我們進一步做模型在養老險與年金商品為因應長壽風險而提撥額外準備金之應用，比較我們模型與B&H的模型下之結果。
在第二篇裡，我們在第一篇模型之period-cohort波動率加入年齡特性成為age-period-cohort波動率，然後用英國女性死亡率資料實證估計這兩種波動率。我們也用實證估計出的波動率計算第一篇定義的資本適足比率(CAR)。
The dissertation contains two essays to focus on a mortality model and make an application to the management of longevity risk. The first essay proposes an additive continuous-time stochastic mortality model which revises that (B&H model) of Ballotta and Haberman (2006) since there are two questionable features in the B&H model. We further demonstrate an application of our model by calculating reserves of longevity risks for pure endowments and various common annuity products in the UK. We also compare our results with those of the B&H model.
The second essay incorporates age-specific effects into period-cohort volatilities in the first essay and empirically estimates the volatilities by using UK female mortality data. We also calculate the empirical capital adequacy ratio (CAR) defined in the first essay by using the empirical estimated age-period-cohort volatilities.
Part I References
Ballotta, L., and Haberman, S., 2006. The fair valuation problem of guaranteed annuity options: the stochastic mortality environment case. Insurance: Mathematics and Economics 38, 195-214.
Bauer, D., Börger, M., and Ruβ, J., 2008. On the pricing of longevity-linked Securities.Working Paper.
Biffis, E., 2005. Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics 37, 443-468.
Blake, D., and Burrows, W., 2001. Survivor bonds: helping to hedge mortality risk. Journal of Risk and Insurance 63, 339-348.
Blake, D., Cairns, A., Dowd, K., and MacMinn, R., 2006. Longevity bonds: financialengineering, valuation, and hedging. Journal of Risk and Insurance 73, 647-672.
Blake, D., Dowd, K., and Cairns, A., 2008. Longevity risk and the Grim Reaper’stoxic tail: the survival fan charts. Insurance: Mathematics and Economics 42, 1062-1066.
Cairns, A. J. G., Blake, D., and Dowd, K., 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., Blake, D., Dowd, K., Goughlan, G. D., Epstein, D., Ong, A., and Balevich, I., 2007. A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. Pensions Institute Discussion Paper I-0701. (http://www.pensions-institute.org/workingpapers/wp0701.pdf)
Dahl, M., 2004. Stochastic mortality in life insurance: market reserves andmortality-linked insurance contracts. Insurance: Mathematics and Economics 35, 113-136.
Denuit, M. H., Devolder, P., and Goderniaux, A.C., 2007. Securitization of longevityrisk: pricing survivor bonds with Wang transform in the Lee-Carter framework. Journal of Risk and Insurance 74, 87-113
Dowd, K., Blake, D., Cairns, A. J. G., and Dawson, P., 2006a. Suvivor swaps. Journalof Risk and Insurance 73, 1-17.
Dowd, K., Cairns, A. J. G., and Blake, D., 2006b. Mortality-dependent financial risk measures. Insurance: Mathematics and Economics 38, 427-440.
Hainaut, D., and Devolder, P., 2008. Mortality modelling with Lévy process.Insurance: Mathematics and Economics 42, 409-418.
Hári, N., Waegenaere A., Melenberg, B., and Nijman, T. E., 2008. Longevity risk in portfolios of pension annuities. Insurance: Mathematics and Economics 42, 505-519.
Lee, R. D., and L. R. Carter, 1992. Modelling and forecasting U.S. mortality. Journal of the American Statistical Association 87, 659-671.
Lin, Y., and S. H. Cox, 2005. Securitization of mortality risks in life annuity. Journal of Risk and Insurance 72, 227-252.
Milevsky, M. A., and Promislow, S. D., 2001. Mortality derivatives and the option to annuities. Insurance: Mathematics and Economics 29, 299-318.
Neves, C., and Migon, H. S., 2007. Bayesian graduation of mortality rates: an application to reserve evaluation. Insurance: Mathematics and Economics 40, 424-434.
Renshaw, A. E., amd S. Haberman, 2003. Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics 33, 255-272.
Schrager, D. F., 2006. Affine stochastic mortality. Insurance: Mathematics and Economics 38, 81-97.
Sithole, T.Z., Haberman, S., Verrall, R.J., 2000. An investigation into parametric models for mortality projections, with applications to immediate annuitants’ and life office pensioners’ data. Insurance: Mathematics and Economics 27, 285-312.

Part II References
Ballotta, L., Haberman, S., 2006. The fair valuation problem of guaranteed annuity options: the stochastic mortality environment case. Insurance: Mathematics and Economics 38, 195-214.
Blake, D., Dowd, K., Cairns, A., 2008. Longevity risk and the Grim Reaper’s toxic tail: the survival fan charts. Insurance: Mathematics and Economics 42, 1062-1066.
Cairns, A. J. G., Blake, D., Dowd, K., 2006. A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance 73, 687-718.
Chen, H., Cox, S.H., 2009. Modeling mortality with jumps: Applications to mortality securitization. Journal of Risk and Insurance 76, 727-751.
Cox, S.H., Lin, Y., Pedersen, H., 2010. Mortality risk modeling: Applications to insurance securitization. Insurance: Mathematics and Economics 46, 242-253.
Dowd, K., Blake, D., Cairns, A. J. G., and Dawson, P., 2006a. Survivor swaps. Journal of Risk and Insurance 73, 1-17.
Dowd, K., Cairns, A. J. G., and Blake, D., 2006b. Mortality-dependent financial risk measures. Insurance: Mathematics and Economics 38, 427-440.
Haberman, S., Renshaw, A., 2009. On age-periods-cohort parametric mortality rate projections. Insurance: Mathematics and Economics 45, 255-270.
Hári, N., Waegenaere A., Melenberg, B., Nijman, T. E., 2008. Longevity risk in portfolios of pension annuities. Insurance: Mathematics and Economics 42, 505-519.
Lee, R.D., Carter, L.R., 1992. Modelling and forecasting U.S. mortality. Journal of the American Statistical Association 87, 659-671.
Lin, Y., Cox, S.H., 2005. Securitization of mortality risks in life annuity. Journal of Risk and Insurance 72, 227-252.
Lin, T., Tzeng, L.Y., 2010, An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation. Insurance: Mathematics and Economics 46, 423-435.
Renshaw, A. E., Haberman, S., 2003. Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics 33, 255-272.
Renshaw, A. E., Haberman, S., 2006. A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics 38, 556-570.
Stevens, R., Waegenaere A., Melenberg, B., 2010. Longevity risk in pension annuities with exchange options: The effect of product design. Insurance: Mathematics and Economics 46, 222-234.
Yang, S.S., Yue, J.C., Huang, H., 2010. Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models. Insurance: Mathematics and Economics 46, 254-270.


 
 
 
 
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