人類死亡率的長記憶性分析

Abstract

近年來，長記憶性（Long-memory property）在經濟與財務金融領域受到高度的關注，也因此在長記憶性的研究發展中，許多經濟與財務金融的時間序列均被視為研究對象，然而，保險業相當關注的風險之一—人類死亡率卻尚未被考慮。本篇研究以探討人類死亡率是否具有長記憶性為出發點，利用ARFIMA模型、Whittle概似函數與Robinson檢定統計量研究美國1933年至2005年中25歲至85歲的人類死亡率，發現男性和女性隨年齡增加所造成的死亡率成長具有長記憶性，且若是以傳統的ARIMA模型進行評估，將會造成商品評價與風險控管上的誤判。此外，在研究的過程中亦發現女性隨年齡增加所造成之死亡率成長的平均成長速率有逐年上升的趨勢，相對的，男性卻維持在一固定水準，此現象與女性平均餘命逐年增加的現象並不違背，主要原因為女性25歲的死亡率下降速度較男性為快。

In recent years, long-memory property has gained considerable attention in economic and financial fields. However, although many economic and financial time series have been studied, human mortality, which plays an important role in insurance has not been considered. In this thesis we will analyze the human mortality of 25-year-old to 85-year-old females and males in the U.S. to find out whether it is a long-memory process. After building the ARFIMA model and considering the Whittle likelihood function along with the Robinson test statistic, we found out that both females’ and males’ annual mortality growth rates are indeed long-memory processes. Additionally, if the ARFIMA model is to be replaced by the ARIMA model it would result in misunderstandings in product pricing and risk control. In our thesis, we also found out that females’ mean of annual mortality growth rates increases by generation while males’ remains stable. Nevertheless, this result doesn’t contradict the fact that females’ average residual life becomes longer because females’ 25-year-old mortality rate decreases by generation.