| Abstract: | 隨著醫藥科技等因素的發展，我國國民平均壽命逐年上升，高齡人口的死亡率下降尤為明顯，人口老化速度愈發明顯，國人對於退休生活、醫療需求更形殷切。但壽命增加蘊含不確定性，提高了應對需求的難度，這類型的問題通稱為長壽風險，對商業保險而言，保險公司可能因壽命延長使得年金提領增加而造成資金不足，或是醫療保險的給付增加而造成經營危機；社會保險也可能因為壽命延長而面臨破產的窘境，不得不增加保費、或是減少給付項目。由於老年人的醫療使用量較多，退休後經濟需求也以高齡人口為主，長壽風險的解決多以老年人為目標，使得高齡死亡率模型格外受到重視，再搭配創新金融商品（如延壽年金、風險證券化等），是許多國家解決長壽風險的主要方法之一。 本計畫探討高齡死亡模型，主要分為兩類：關係模型、隨機模型，比較哪些模型適合用於因應長壽風險，考慮的模型包括Gompertz、Coale and Kisker (1990)、Lee and Carter (1992)、Renshaw and Haberman (2006)、Cairns et al. (2006a)以及王信忠與余清祥(2011)提出的模型，其中後者結合工程上可靠度函數Weibull分佈，提出折扣數列比值韋伯模型（DSW）。本文以實證資料評估模型優劣，使用台灣、日本、美國三國五齡組及單齡組死亡率資料，除了估計效果的比較，也以交叉驗證檢驗預測預測結果（短期預測、長期預測）。分析發現Lee and Carter模型有最好的結果，本文提出的DSW模型也不錯，但若死亡率資料為五齡組，則推薦傳統的Gompertz模型。
Prolonging life expectancy is a common phenomenon in the 21st century and taking care of the elderly becomes a major policy issue in many countries. Longevity risk, or the continuing mortality improvement, is the key factor of determining if the financial solvency of these policies. Stochastic mortality models are a popular and powerful tool to deal with the longevity risk. Although their short-term predictions are quite satisfactory, they often fail to provide reliable long-term forecasts. In this project, we plan to enhance the age link between age-specific mortality rates in the stochastic mortality models and improve their long-term predictions. Alternatively, we will also try to modify the relational models (e.g., Gompertz’s Law), adding stochastic factors, and let the modified models can be used in mortality forecasts. We consider two types of mortality models for the elderly, which are relational models and stochastic models, and evaluate which model(s) are suitable for dealing with the longevity risk. Mortality models considered in this study include those by Gompertz, Coale and Kisker (1990), Lee and Carter (1992), Renshaw and Haberman (2006), Cairns et al. (2006a) and Wang and Yue (2011). In specific, we propose using the Weibull distribution to predict discount sequence by Wang and Yue, namely DSW. We use the mortality data from Taiwan, Japan, and U.S. to evaluate these models, via cross-validation. We found that, with respect to estimation and prediction errors, Lee and Carter model is the best, following by the DSW. Also, if the data is in the 5-age format, the traditional Gompertz model is recommended. |
