一类新的失真风险测度及其尾渐近性（重点讨论VaR）
New class of distortion risk measures and their tail asymptotics with emphasis on VaR
摘要：
失真风险度量因其吸引人的性质而被广泛应用于金融和保险领域。给出了构造一类新的偏差函数和偏差测度的三种方法。该方法包括堆肥法、混合法和基于copula理论的方法。次可加性是一个重要的属性时，汇总风险，以保持多样化的好处。然而，风险价值（VaR）作为最著名的失真风险度量的例子并不总是全局次可加的，除了椭圆分布的风险。在本文中，而不是研究次可加性，我们研究的尾部次可加性的风险价值和其他失真的风险措施。特别是，我们证明了风险值是尾部次可加的情况下，风险的支持是有界的。各种例子也被提出来说明结果。
英文摘要：
Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves the composting methods, the mixing methods and the approach that based on the theory of copula. Subadditivity is an important property when aggregating risks in order to preserve the benefits of diversification. However, Value at risk (VaR), as the most well-known example of distortion risk measure is not always globally subadditive, except of elliptically distributed risks. In this paper, instead of study subadditivity we investigate the tail subadditivity for VaR and other distortion risk measures. In particular, we demonstrate that VaR is tail subadditive for the case where the support of risk is bounded. Various examples are also presented to illustrate the results.
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