部分信息下的最坏情况范围风险值

Lujun Li, Hui Shao, Ruodu Wang, Jingping Yang
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引用次数: 31

摘要

在本文中,我们研究了具有给定均值和方差的单一风险模型和集合风险模型中一类一般风险度量——风险范围值(RVaR)的最坏情况,以及每个风险的对称性和/或单峰性。对于不同类型的部分信息设置,分别得到了单一风险模型和聚合风险模型的RVaR的明确界,以及相应的边际风险最坏情景和它们之间对应的联结函数(依赖结构)。与已有文献不同的是,本文采用了一种统一的方法,结合凸序和最近发展的联合可混性概念,得到了不同部分信息设置下的尖锐界。作为特殊情况,直接推导了风险价值(VaR)和尾部风险价值(TVaR)的边界。数值算例也说明了我们的结果。
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Worst-Case Range Value-at-Risk with Partial Information
In this paper, we study the worst-case scenarios of a general class of risk measures, the Range Value-at-Risk (RVaR), in single and aggregate risk models with given mean and variance, as well as symmetry and/or unimodality of each risk. For different types of partial information settings, sharp bounds for RVaR are obtained for single and aggregate risk models, together with the corresponding worst-case scenarios of marginal risks and the corresponding copula functions (dependence structure) among them. Different from the existing literature, the sharp bounds under different partial information settings in this paper are obtained via a unified method combining convex order and the recently developed notion of joint mixability. As particular cases, bounds for Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are derived directly. Numerical examples are also provided to illustrate our results.
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