论文标题
在不确定性下有条件的失真风险措施
On conditional distortion risk measures under uncertainty
论文作者
论文摘要
模型不确定性在风险衡量理论和实践中，例如财务风险管理和监管等实践中一直是一个突出的问题。在本文中，在本文中，我们采取了一个新的观点来描述模型的不确定性，从而提出了模型不确定性下的一类新的风险度量。更确切地说，我们使用辅助随机变量来描述模型不确定性。我们首先在辅助随机变量下建立条件失真风险度量。然后，我们通过提出一组新公理来公理地对其进行表征。此外，研究了其连贯性和双重表示。最后，我们与一些已知的风险措施进行比较，例如风险（WVAR）的加权价值，风险范围值（RVAR）和ES的$ \ sq-$混合物。我们的建模的优点是其灵活性，因为辅助随机变量可以描述包括模型不确定性在内的各种环境。为了说明所提出的框架，我们还在存在背景风险的情况下推断出新的风险措施。本文为模型不确定性下的风险措施提供了一些理论上的结果，预计将对模型不确定性下的风险措施进行有意义的补充。
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the model uncertainty, and thus propose a new class of risk measures under model uncertainty. More precisely, we use an auxiliary random variable to describe the model uncertainty. We first establish a conditional distortion risk measure under an auxiliary random variable. Then we axiomatically characterize it by proposing a set of new axioms. Moreover, its coherence and dual representation are investigated. Finally, we make comparisons with some known risk measures such as weighted value at risk (WVaR), range value at risk (RVaR) and $\sQ-$ mixture of ES. One advantage of our modeling is in its flexibility, as the auxiliary random variable can describe various contexts including model uncertainty. To illustrate the proposed framework, we also deduce new risk measures in the presence of background risk.This paper provides some theoretical results about risk measures under model uncertainty, being expected to make meaningful complement to the study of risk measures under model uncertainty.
