Lee-Carter 模型下死亡率預測之改善與其在確定提撥制退休金的應用

Improvement on Mortality Predictions Using the Lee-Carter Model and Its Application to A Defined Contribution Pension Plan

長命風險是現代人所面臨的重大議題，而準確的預測死亡率是能夠有效管理長命風險的關鍵因素之一。Lee-Carter模型(Lee and Carter 1992)是最被廣泛應用以及討論的死亡率模型，然而，在參數配適過程當中，使用者往往假設對數死亡率的改善速度是固定的，沒有捕捉到改善速度隨著時間變化的現象。本研究提出利用時間加權估計模型參數，以捕捉死亡率改善趨勢的變化，並提升Lee-Carter模型的預測能力。我們並探討在確定提撥退休金制度下，死亡率預測方法的差異對於資產配置的影響；在固定的提撥率以及考慮死亡率的改善速度下，個人必需進行更積極的資產配置以滿足退休後所需要的資金需求。

Accurately predicting mortality is central in reducing longevity risk. Among various mortality models, the Lee-Carter model (Lee and Carter 1992) is the most popular and has been widely applied and discussed. One criticism of the Lee-Carter model is that it assumes a fixed rate of decline (improvement) in the logarithm of mortality rates when using the common singular value decomposition (SVD) approach, and does not capture the trend of mortality improvements over time. This study proposes using a time adjustment weight to enhance the prediction performance of the Lee-Carter model, and to capture the trend of mortality improvements. Additionally, we examine the effect of different mortality predicttion methods on the optimal asset allocation for a Defined Contribution pension plan. For a given contribution rate, an aggressive investment strategy is appropriate when considering the trend of mortality improvements.