利率的變動、解約率的變化以及死亡率的不確定性皆會對壽險保單責任準備金產生影響，本研究以有效存續期間的方法來衡量壽險保單責任準備金的利率風險及死亡率風險。死亡率的隨機性是採用CBD隨機死亡率模型(Cairns et al.(2006))與Lee-Carter死亡率模型(Carter and Lee (1992))來估計；利率隨機性是採用CIR利率模型(Cox, Ingersoll, and Ross (1985))；利率對解約率的動態是依據反正切利差解約率模型(Babbel et al. (2002)與Kim (2005))。本研究所探討的保單包括死亡險、生存險、生死合險與增額壽險，研究結果發現CBD模型在死亡險、生死合險與增額壽險時會產生死亡率風險造成準備金提高，Lee-Carter模型在生存險時會產生死亡率風險造成準備金提高。死亡險準備金與保單到期期限關係圖呈現初期正相關後期負相關的凹函數關係圖。有效存續期間於準備金越接近零時會產生絕對值越大的異常值。利用準備金的變動發現在死亡險之利率風險大於死亡率風險，生存險與生死合險則相反，而增
額壽險為一半大於一半小於。

Our research use effective duration to measure the interest rate risk and the mortality risk of life insurance policy reverses, because of the changes in interest rates, surrender rate, and the uncertainly mortality should affect the life insurance policy reverses. We use CBD stochastic mortality (Cairns et al.(2006)) model and Lee-Carter mortality model (Carter and Lee (1992)) estimate the stochastic mortality. We also use CIR interest rate model (Cox, Ingersoll, and Ross (1985)) to simulate the stochastic interest rate； And a general surrender rate model (Babbel et al. (2002)) to measure the movement surrender rate from interest rate. Analyze term life insurance, endowment, pure endowment policies, and increase insurance, and result show that risk of death in the CBD model with the term life insurance, pure endowment and increase insurance will generate an increase the reserves for policies, and Lee-Carter model in endowment will produce mortality risk to generate an increase the reserves for policies. Term life insurance reserves with time to maturity showing a positive correlation in early and negative correlation in late. When the policy reverses closer to zero, we will have the greater absolute value outliers in effective duration. We use find the interest rate risk greater than the mortality risk in the term life insurance, but the endowment and pure endowment policies are contrast, the increase insurance half is greater and half is less by the change of the reverses

Anthony M. Santomero and David F. Babbel “Financial Risk Management by Insurers: An Analysis of the Process.” The Journal of Risk and Insurance. Vol. 64 NO. 2, (1997), pp. 231-270
Benjamin Gompertz,” On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies” Philosophical Transactions of the Royal Society of London, Vol. 115, (1825), pp. 513-583
Bierwag G.O., G. Kaufman George, and Alden Toevs “Duration: Its Development and Use in Bond Portfolio Management.” Financial Analysts Journal,(1983)
Brillinger, D.R. “The Natural Variability of Vital Rates and Associated Statistics.” Biometrics 42, (1986)
Bierwag, G. O.,”Duration Analysis: Managing Interest Rate Risk.” BalIinger, Cambridge, MA. (1987).
Babbel, D. F., J. Gold, and Merrill C., “Fair Value of Liabilities:” The Financial Economics Perspective, North American Actuarial Journal. (2002)
Cairns, A.J.G., Blake, D., and Dowd, K. “A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration”, Journal of Risk and Insurance, 73: 687-718. (2006)
Cairns, A.J.G., Blake, D., and Dowd, K., Coughlan, G.D., Epstein, D., Ong, A., and Balevich, I. “A quantitative comparison of stochastic mortality models using data from England & Wales and the Unites States,” Pensions Institute Discussion Paper PI-0701, (2007)
Eric Briys and Francois de Varenne “Valuing Risky Fixed Rate Debt: An Extension.” Journal of Financial and Quantitative Analysis, Vol. 32, No. 2, (1997), pp. 239-248
Frank K . Reilly, J. Wright David, and Robert R. Johnson “Analysis of the Interest Rate Sensitivity of Common Stocks” The Journal of Portfolio Management, Vol. 33, No. 3, (2007),pp. 85-107
GO Bierwag, GG Kaufman and A Toevs, “Duration: its development and use in bond portfolio management” Financial Analysts Journal, (1983)
Hamelink C, O Tjurmina, Damadzic R, WS Young, Weihe E, HW Lee, Eiden LE, “Pituitary adenylate cyclase-activating polypeptide is a sympathoadrenal neurotransmitter involved in catecholamine regulation and glucohomeostasis”. Proc Natl Acad Sci USA 99:461–466. (2002)
John C. Cox, E. Ingersoll Jonathan, Jr. and Stephen A. Ross, ” A Theory of the Term Structure of Interest Rates”, Econometrica, Vol. 53, No. 2 (Mar., 1985), pp. 385-407
Kim, Changki, “Modeling surrender and lapse rates with economic variables,” North American Actuarial Journal 9, (2005), pp. 56-70.
Ronald D. Carter and Lawrence R. Lee, ” Modeling and Forecasting U. S. Mortality” Journal of the American Statistical Association, Vol. 87, No. 419 (Sep., 1992), pp. 659-671
Richard MacMinn, Krzysztof Ostaszewski, Ranee Thiagarajah and Jan Frederik Weber, “Mortality improvement select birth cohorts and their effect on pricing of survival bonds” (2008)
Tsai, Chenghsien, “The term structure of reserve durations and the duration of aggregate reserves.” Journal of Risk and Insurance 76, (2009), 419-441.
Vasicek, O., "An Equilibrium Characterization of the Term Structure." Journal of Financial Economics, Volume 5, Issue 2, (1977), Pages 177-188
蔡政憲、何憲章、鄒治華，”壽險保單之存續期間分析”(2002)
曾奕翔、余清祥，”Lee-Carter估計模式與死亡率推估研究” (2005)
劉祐如，”CBD隨機死亡率模型世代效應之研究” (2009)
詹芳書，“壽險保單準備金之有效存續期間分析” (2009)