GlueVaR失真风险度量下的最优再保险（英文）  

Optimal Reinsurance under GlueVaR Distortion Risk Measures

作　　者：王文元[1,2] 肖立群[3] 

机构地区：[1]新疆财经大学应用数学学院,乌鲁木齐830012 [2]厦门大学数学科学学院,厦门361005 [3]广州大学经济与统计学院,广州510006

出　　处：《应用概率统计》2017年第3期267-284,共18页Chinese Journal of Applied Probability and Statistics

基　　金：supported in part by the National Natural Science Foundation of China(Grant Nos.11401498;11601097);the Fundamental Research Funds for the Central Universities of China(Grant No.20720140525)

摘　　要：受到文献[1]和文献[2]的启发,本文从保险人的角度,研究了GlueVaR失真风险度量下的最优再保险问题.假设保险标的的损失为X,保险人为分散风险签订了以索赔总额为计算基础的分保合同.按合同,分保人承担的风险为f(X),保险人承担剩下的风险X-f(X).此外基于期望保费原则,保险人需支付分保人再保险费(1+ρ)E[f(X)](其中ρ为安全负载系数).采用文献[2]中的技术方法,我们得出此时最优转移损失函数是一类增凸函数.从而可知最优再保险策略为停止损失再保险.Motivated by [1] and [2], we study in this paper the optimal （from the insurer,s pointof view） reinsurance problem when risk is measured by a general risk measure, namely the GlueVaR distortion risk measures which is firstly proposed by [3]. Suppose an insurer is exposed to the risk X and decides to buy a reinsurance contract written on the total claim amounts basis, i.e. the reinsurer covers f （X） and the cedent covers X - f （X ）. In addition, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the reinsurance premium, （1 ＋ p）E[f （X）] （p is the safety loading）, under the expectation premium principle. Based on a technique used in [2], this paper derives the optimal ceded loss functions in a class of increasing convex ceded loss functions. I t turns out that the optimal ceded loss function is of stop-loss type.

关 键 词：最优再保险 Glue风险价值 失真风险度量 转移损失函数 

分 类 号：O211.9[理学—概率论与数理统计]