預測年齡死亡率之比較研究

Abstract

隨著人口結構的變化和社會老齡化的加劇，死亡率的建模和預測越來越受到關注，特別是在保險領域，準確預測死亡率有助於保險公司有效制定保單。在這項研究中，我們從Lee-Carter 模型出發，將原始的奇異值分解拓展到函數型奇異值分解，進而得到與時間和年齡有關的一對奇異函數，接著我們根據年份相關的奇異函數進行局部線性外推做預測，並將其預測表現與Lee-Carter模型進行比較。在實際數據分析中，我們使用了台灣的死亡率數據，結果我們的預測結果比Lee-Carter模型更準確，在模擬實驗亦得到相同的結論。

With demographic changes and society aging, the modeling and prediction of mortality rates have garnered increasing attention, especially in the insurance sector. Accurate mortality forecasts assist insurance companies in formulating policies effectively. In this study, we begin with the Lee-Carter model and extend the original singular value decomposition to a functional version, yielding a pair of time-specific and age-specific singular functions. Subsequently, we conduct local linear extrapolation based on these year-specific singular functions for forecasting, comparing their performance with that of the Lee-Carter model. In our real data analysis, we use mortality data from Taiwan to demonstrate that our forecasting performance is more accurate than that of the Lee-Carter model. This conclusion is further supported by our simulation study.