死亡率模型之比較：以臺灣資料為例

死亡率模型之探討是保險精算領域重要之研究課題，近年來國際上有許多新模型發展，然而相關文獻鮮少使用臺灣資料進行實證。本研究介紹幾個比較新穎的模型，提供我國保險公司參考，包括Plat於2009年提出的M9、O'Hare與Li於2012年提出的M10、Mitchell et al.於2013年提出的Mc-1與Mc-2等，利用Human Mortality Database（HMD）資料庫1970-2014年之20-90歲臺灣單齡組死亡率資料進行配適與預測，並考慮非高斯分配（variance gamma分配、normal inverse Gaussian分配、skewed t分配）於Mc-1以及Mc-2模型之期間效果以檢視兩模型之預測能力。研究結果發現在配適能力上，若以殘差平方和平方根（root sum of squared errors, RSSE）作為衡量標準，男性資料適合Mc-2模型，女性資料適合M9模型。在死亡率趨勢中，若以Akaike information criterion（AIC_c）為衡量基礎，女性資料存在非高斯分配之特性。在模型預測能力上，不論以RSSE或平均絕對百分比誤差（mean absolute percentage error, MAPE）作為衡量標準，男性資料皆以Mc-2模型最佳，女性則以M10模型最佳，且預測之對數死亡率95%信賴區間大多皆包含樣本外資料。整體而言，本文建議臺灣死亡率男性資料適合Mitchell et al.於2013年提出之Mc-2模型，而女性資料則適合用M10模型。

關鍵字

死亡率模型；非高斯分配；期間效果

並列摘要

We investigate how new mortality models perform with Taiwanese mortality data. Although much progress has been made in the mortality model literature, practitioners still adopt the Lee-Carter model (1992) for the mortality forecast of the Taiwanese population. We compare the recently developed Mitchell et al. (2013) models with one- and two-factor models, namely Mc-1 and Mc-2, that incorporate heavy-tailed distributions such as variance gamma, normal inverse Gaussian, and skewed t distributions into period effects with two increasingly popular parametric models with cohort effects, namely the M9 and M10 models. Using age-specific mortality rates from Human Mortality Database (HMD), we show that the female mortality trend in Taiwan is non-Gaussian, as the model selection criteria such as AIC_c strongly support this. Our results suggest the two-factor Mitchell et al. (2013) model captures the male mortality rates better, while the M10 model performs better for female mortality rates in terms of root sum of squared errors (RSSE) and mean absolute percentage error (MAPE).

並列關鍵字

mortality models ； non-gaussian distributions ； period effects

參考文獻

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