高年齡層死亡率增加幅度趨緩對保險經營之影響The Impact of Elderly Mortality Deceleration on Life Insurance

摘要
近十年來，台灣地區人口老化日趨明顯，老年死亡率之推估亦為一相關的重要議題。以往利用Gompertz模型之假設來配適高年齡層之死亡率即可得到不錯之結果，然而隨著平均壽命的提高，近年之研究皆指出Gompertz在高年齡層有高估的現象，再加上實證研究發現已開發國家在高年齡層死亡率隨年齡之增加幅度有趨緩之現象，因此若繼續使用該假設來預估高年齡層之死亡率，理論上對於保險公司之年金商品，勢必低估該年齡層之生存率，造成保費與提存準備金之不足，而增加喪失清償能力的機會；加以死亡率逐年改善之趨勢，對年金商品來說，這些問題勢必擴大。因此本文以日本女性死亡率為實證資料，利用Weon提出之模型來和Gompertz模型做進一步比較，分析在兩種模型假設下，所預估高年齡層死亡率之差異及對壽險商品之影響。
關鍵字：Gompertz模型、Weon模型、特徵壽命、死力趨緩、直角化
Abstract
The trends of aging in Taiwan become obvious in last ten years. The estimate of elderly mortality rates is one of the related studies. Gompertz model for the mortality rate provided well fitness to mortality data even at the elder ages in the past. But its estimates were found to be overestimated recently. There are evidences from many developed countries that the incremental rate in mortality decelerates at high ages. Therefore, estimating elderly mortality rate under the Gompertz model will cause the underestimates in survival rates and premiums and inadequacies in reserves for the annuity products; especially, the improvement in mortality rates makes the problem of inadequacies in reserves more seriously. In this paper, basing on female mortality rates of Japanese, we compare the fitness of Gompertz model with those of Weon model to show the inadequacies of Gompertz model for the mortality rate at elder ages. Also, using the expected mortality rate produced by these two models separately as actuarial assumptions, we analyze the impacts on life insurance operations.
Keywords: gompertz model, weon model, characteristic life, mortality deceleration, rectangularization