EAGER: Conditional Risk Measures for Reducing Cascading Failures

在一个相互依赖的系统中(如电网和金融市场)，不良事件可能蔓延并造成更严重的经济和/或社会后果，也称为连锁故障。典型的例子包括2003年美国东北部因输电线路故障而引发的停电，以及最近由美国次级抵押贷款市场引发的全球经济衰退。为了保护一个相互依赖的系统，系统操作员需要更好地了解当不良情况发生时连锁故障的威胁，并相应地制定更好的操作和补救计划。这一早期概念探索性研究(AGER)奖支持探索性研究，以研究量化连锁故障威胁的条件风险衡量标准，并展示它们如何在许多实际应用中帮助改善运营决策。该项目的成功实施将为系统运营商提供有效的决策支持工具，以识别连锁故障并减少潜在影响。同时，该项目将为相关研究课题的本科生和研究生课程提供新的教材。代表不足的博士生将被激励参与研究和教育活动。这个项目的目的是探索一类条件风险度量，它概括了许多经典的风险度量，包括条件风险价值。由于商的表达式和分布的模糊性，将这些条件风险度量纳入随机优化模型在技术上是具有挑战性的。该项目将探索在数据驱动的背景下重新制定和近似的方法。更具体地说，将探索条件风险度量的分布稳健版本及其在各种分布模糊设置下的重构，将研究基于可用历史数据的条件风险度量的样本近似，并将制定有效的求解算法来处理条件风险度量。该项目的成功完成将带来随机优化文献中的新知识，包括函数优化分析、历史数据的值以及随机整数规划的割平面。

In an interdependent system (e.g., power grids and financial markets), an undesirable event could spread and cause even more severe economic and/or social consequences, also known as cascading failures. Typical examples include the blackout in Northeastern America triggered by a tripped transmission line in 2003, and the recent global recession stemming from the U.S. subprime mortgage market. To protect an interdependent system, a system operator need to better understand the threats of cascading failures when undesirable conditions are realized, and accordingly make better operational and recourse plans. This EArly-concept Grant for Exploratory Research (EAGER) award supports exploratory research to study conditional risk measures on quantifying the threats of cascading failures, and show how they can help improve operational decision makings in many practical applications. The successful implementation of this project will provide effective decision support tools for system operators to identify cascading failures and reduce potential impacts. At meanwhile, this project will provide new teaching materials for undergraduate- and graduate-level courses on related research topics. Underrepresented Ph.D. students will be motivated to participate in the research and educational activities. This project aims to explore a class of conditional risk measures which generalize many classical risk measures including the Conditional Value-at-Risk. Because of the quotient expressions and the distributional ambiguity, it is technically challenging to incorporate these conditional risk measures in stochastic optimization models. This project will explore reformulation and approximation approaches in a data-driven context. More specifically, distributional robust versions of the conditional risk measures and their reformulations under various distributional ambiguity settings will be explored, sample approximations of the conditional risk measures based on available historical data will be investigated, and effective solution algorithms to handle the conditional risk measures will be formulated. The successful completion of this project will lead to new knowledge in the stochastic optimization literature, including functional optimization analyses, the value of historical data, and cutting planes for stochastic integer programs.