论文标题
定量统计鲁棒性依赖尾部的法律不变风险措施
Quantitative Statistical Robustness for Tail-Dependent Law Invariant Risk Measures
论文作者
论文摘要
当通过经验数据或蒙特卡洛模拟通过尾巴依赖的法律风险措施（例如，有条件的危险价值（CVAR））估算财务状况的风险时，重要的是要确保统计估计器的稳健性，尤其是当数据包含噪声时。 KR Atscher等。 [1]提出了一个新框架，以检查估计量依赖尾部的定性鲁棒性在Orlicz空间上的不变风险度量，这离早期研究的较远，用于研究Cont等人的风险测量程序的鲁棒性。 [2]。在本文中，我们遵循研究流，提出了一种定量方法，以验证依赖尾巴的法律不变风险度量的统计鲁棒性。我们方法的一个独特特征是，我们使用较近期的指标来量化真正的潜在概率度量的变化，以分析法律插件估计量之间的差异，该法律规律不变性风险措施的定律基于真实的数据和扰动数据的差异，这使我们能够在风险范围内与差异相比，这使我们能够与差异相比，这使我们能够与差异相关。此外，新引入的Lipschitz连续性概念使我们能够检查依赖尾巴的风险度量的鲁棒性程度。最后，我们将定量方法应用于一些众所周知的风险措施来说明我们的理论。
When estimating the risk of a financial position with empirical data or Monte Carlo simulations via a tail-dependent law invariant risk measure such as the Conditional Value-at-Risk (CVaR), it is important to ensure the robustness of the statistical estimator particularly when the data contain noise. Kratscher et al. [1] propose a new framework to examine the qualitative robustness of estimators for tail-dependent law invariant risk measures on Orlicz spaces, which is a step further from earlier work for studying the robustness of risk measurement procedures by Cont et al. [2]. In this paper, we follow the stream of research to propose a quantitative approach for verifying the statistical robustness of tail-dependent law invariant risk measures. A distinct feature of our approach is that we use the Fortet-Mourier metric to quantify the variation of the true underlying probability measure in the analysis of the discrepancy between the laws of the plug-in estimators of law invariant risk measure based on the true data and perturbed data, which enables us to derive an explicit error bound for the discrepancy when the risk functional is Lipschitz continuous with respect to a class of admissible laws. Moreover, the newly introduced notion of Lipschitz continuity allows us to examine the degree of robustness for tail-dependent risk measures. Finally, we apply our quantitative approach to some well-known risk measures to illustrate our theory.
