投資型保險保證給付風險之衡量：同調風險衡量值的介紹與應用

風險值(VaR)為研究上常用來量化投資型保險保證給付風險的衡量指標。然而，Wirch(1999)指出由於風險值存在不滿足Artzner et al.(1999a)所定義出之同調風險衡量值的特性，其在量化風險上會產生一些問題。Wirch and Hardy(1999)在其研究中找出符合同調性質之風險量化指標如尾部風險值、比例危險及雙重次方變形函數風險衡量值以供風險衡量上的應用。因此，本研究針對國外文獻中已發展之同調風險衡量值的觀念做一介紹，並將其應用在投資型保險之準備金提存上。本研究利用蒙地卡羅方法模擬出投資保證成本之機率分配，再利用Wirch and Hardy(1999)所建議的同調風險衡量值做為準備金提存法則，數值例子以英國近年來保險公司所面臨保證年金選擇權之單連保單進行探討，並針對其以同調風險衡量準備金提存之數值結果和風險值的差異性進行分析。
關鍵字：同調風險衡量值、變形函數、保證年金選擇權

Measuring Guaranteed Risk for Investment-Linked Insurance: An Introduction to Coherent Risk Measure and Its Application

　　　　　　　　　　　　(Sharon S. Yang)＊(Hong-Chih Huang)＊(Yu-Hung Cheng)

Value at Risk (VaR) is a common risk measure to quantify guaranteed risk for investment-linked insurance. However, Wirch (1999) pointed out that VaR does not adhere to the coherency requirements introduced by Artzner et al. (1999a) and discussed the implications of this finding. In this paper, we survey the main concepts of recent developments in coherent risk measures in risk management for investment guarantees with life insurance. We consider coherent risk measures for reserves for guaranteed annuity options. Finally, comparisons of numerical results for VaR and coherent risk measures are analyzed.
Keywords: coherent risk measure, distortion functions, guaranteed annuity options