Systemic and Systematic Risks-Driven Marginal Expected Side-effect

System-wide stress events (SWSE) can occur in social, economic, financial, environmental, medical, and many other systems. An SWSE can cause severe damage to some or all members in the system. Understanding and measuring the marginal expected side-effect (MES) for each member caused by an SWSE can lead to better risk management and decision-making. This paper defines an SWSE as a scenario in which either a representative systematic index or the index of the worst-performing member (systemic index) in a system exceeds its respective prescribed threshold. This broadened SWSE definition introduces an innovative systemic and systematic risks-driven marginal expected side-effect (SYS2MES) index. We construct estimators for SYS2MES and establish their asymptotic theories within the multivariate extreme value theory framework, including tail dependent and tail independent scenarios, thereby enhancing its applicability to a wide range of models. The finite sample performance of the estimators is investigated in a simulation study. The advantages of SYS2MES are demonstrated by studying its application to Dow Jones’ 30 stocks and COVID-19 data in the United States, yielding more meaningful results than existing approaches.全系统压力事件（System-wide Stress Events, SWSE）可出现于社会、经济、金融、环境、医疗等多个领域的系统之中。此类事件可对系统内部分乃至全部成员造成严重损害。对全系统压力事件引发的各成员边际预期副作用（Marginal Expected Side-effect, MES）进行理解与测算，有助于优化风险管理与决策制定。本文将全系统压力事件定义为如下场景：当系统内具有代表性的系统性指标，或是表现最差的成员的指标（系统性指标）突破各自预设阈值时，即构成全系统压力事件。这一拓展后的全系统压力事件定义，提出了一种创新性的、由整体系统性与系统化风险驱动的边际预期副作用（SYS2MES）指数。我们针对SYS2MES构建了估计量，并在多元极值理论框架下建立了其渐近理论，涵盖尾部相依与尾部独立两类场景，由此提升了该方法对多种模型的适用性。我们通过模拟实验探究了该估计量的有限样本表现。通过将SYS2MES应用于美国道琼斯30种成分股与新冠疫情相关数据，我们验证了该指数的优势，其所得结果相较于现有方法更具现实参考价值。