自二十世紀中葉以來，人類平均壽命屢創歷史紀錄，高齡（65歲以上）人口在許多國家已經或即將超過全國人口的五分之一，老年族群成為二十一世紀的熱門研究議題。然而，由於高齡人口資料在1990年代以後才有較完整紀錄，對於何種高齡死亡率模型為較佳，至今仍無定論。本文引入吃角子老虎問題（Bandit Problem）的規律折扣數列（Regular Discount Sequence），用來描述老年人的平均餘命變化，以及預測未來的高齡死亡率。許多常用的死亡率模型，例如：Gompertz法則、均勻死亡假設（Uniform Distribution of Death）、定死力假設（Constant Force）、以及雙曲線假設（Hyperbolic）等，都滿足規律折扣數列的條件。除了理論推導之外，我們採用美國加州大學柏克萊分校（University of California, Berkeley）的Human Mortality Database（HMD）資料庫，包括臺灣、日本及美國的死亡率資料，驗證規律折扣數列，三個國家的生存數與平均餘命均大致符合折扣數列的假設。另外，我們也使用布朗運動（Brownian Motion）隨機微分方程式，建立折扣數列模型，用來預測未來的高齡人口死亡率，電腦模擬顯示無論是數列比值或是死亡率預測，折扣數列模型都有不錯的結果，亦即本文提出的模型可用於預測高齡死亡率。

Life expectancies of the human male and female have been increasing significantly since the turn of the 20th century, and the trend is expected to continue. The study of elderly mortality has thus become a favorite research topic. However, because there were not enough elderly data before 1990, there is still no conclusion about which mortality model is appropriate for describing elderly mortality. In this study, we modify the regular discount sequence in the Bandit Problem and use it to describe elderly mortality. We found that many frequently used mortality models, such as the Gompertz Law, and famous mortality assumptions (Uniform Distribution of Death, Constant Force, and Hyperbolic assumption) all satisfy the requirement of a regular discount sequence.We also use empirical data from the HMD (Human Mortality Database from University of California, Berkeley), including data from Japan, the US, and Taiwan, to evaluate the proposed approach. The discount sequences of life expectancy and surviving number ratio do satisfy the regularity condition. In addition, we use the Brownian Motion Stochastic Differential Equation to model the discount sequence. Using this model, we predict the future mortality rates and life expectancy. The simulation study shows some promising results.