Riskiness在人身保險商品之風險控管上的應用

Abstract

傳統上用來衡量風險的指標，不外乎是標準差、變異數、夏普指標及風險值等，但這些指標卻都有其缺失與不足之處。因此Aumann與Serrano（2008）在Journal of Political Economy提出了一個全新的風險指標─「Riskiness」，該指標具有諸多良好的經濟性質，如符合對偶性和正齊次性，此外還具備一階隨機單調及二階隨機單調，加上計算過程也相當容易。 本論文即是將該具備諸多良好性質的指標分別應用在四大人身保險商品（死亡保險、生存保險、生死合險及年金保險）上，計算此四類保險商品在不同情境假設下之Riskiness，並探討其變化，使保險公司能將此結果運用在保單設計的實務上，極小化其所承擔的風險。 研究結果顯示繳費方式為躉繳之生死合險的Riskiness遠低於死亡保險及生存保險，而年金保險的趨勢大抵和生存保險相同，死亡保險的趨勢則和生存保險完全相反。此外男性之Riskiness除了在死亡保險較女性低外，其餘均較女性高。

When measuring the risk, we usually use standard deviation, variance, Sharpe ratio, value at risk, etc. However, there are a lot of drawbacks in these risk indices. For this reason, Aumann and Serrano brought a new risk index called “Riskiness” at Journal of Political Economy in 2008. “Riskiness” contains a large number of good economic characters. It satisfies duality and positive homogeneity. In addition, it is also provided with first-order monotonic and second-order monotonic. Moreover, its calculation process is not too complicated to use. In this paper, I apply this new risk index “Riskiness” on the life insurance products, including life insurance, pure endowment, endowment insurance and annuity. The main purpose of this paper is to see how factors affect the riskiness under different assumptions. The insurance companies can use these results to apply on the design of the products, and minimize their risks. Research results show that the riskiness of endowment insurance is much lower than life insurance and pure endowment when the premiums are single payment. The trend of annuity is identical with pure endowment, and the trend of life insurance is opposite to pure endowment. Moreover, the riskiness of male is lower than female in life insurance, but higher in the other three insurances.