臺灣的男女死亡率皆呈現逐年遞減的趨勢，自1993年進入高齡化社會後，預計將會在2018年進入高齡社會；人口不斷老化的結果讓社會上不論人民或是如保險公司等年金提供者皆面臨愈來愈嚴重的長壽風險；目前現有文獻提出了許多方式以解決長壽風險，其中多數的方法皆需使用到對未來死亡率之預估。 本研究為了能夠更準確的預估未來死亡率的趨勢，參考了Lee Carter (1992)所提出之模型以及Li and Lee (2005)、Li (2013)提出之共同改善趨勢效果，提出考慮商品與商品間以及商品與整體人口間共同改善趨勢之死亡率模型；本研究利用臺灣之保險公司壽險及年金業務經驗死亡率和Human Mortality Database之臺灣人口資料對模型進行配適，並以MAE、MAPE、RMSE三項指標比較與Lee Carter模型之優劣。 最後，本研究利用所配適之模型進行預測，模擬自然避險之效果，檢視臺灣保險業進行自然避險的可能效益，並對決策者在於決定是否要進行自然避險方面給出建議。 / Taiwan became an aging society in 1993 and is expected to become an aged society in 2018. The progressive decrease in Taiwan mortality since the 20th century for both genders has made longevity risk a serious problem for both people and annuity provider in Taiwan. So far, the literature has discussed about how to deal with longevity risk and came out with several solutions which can be categorize as “industry self-insurance”, “ mortality projection improvement” and “capital market solutions” , most of them are related to the projection of mortality. In order to provide a more precise projection of future mortality trend, this article designs several models which collaborates Lee Carter Model (1992) and the common improvement trend suggested by Li and Lee (2005). Based on our models, the Taiwan insurance industry experience mortality data and the Taiwan population mortality data, we test the performance of our models and make comparison. Lastly, we use the model we find to project future mortality trend and try to make a simulation of natural hedging strategy in Taiwan. The purpose we do this is to test the performance of natural hedging method and give suggestion for the decision-maker when they are considering whether to execute a natural hedging strategy.

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.