EAGER: Conditional Risk Measures for Reducing Cascading Failures

在相互依赖的系统中（例如，电网和金融市场），不良事件可能蔓延并导致更严重的经济和/或社会后果，也称为级联故障。2003年因输电线路故障导致的美国东北部大停电和最近因美国次级抵押贷款市场引发的全球经济衰退就是典型的例子。为了保护相互依赖的系统，系统操作人员需要更好地了解当不良情况发生时级联故障的威胁，并相应地制定更好的操作和追索计划。该奖项支持探索性研究，以研究量化级联故障威胁的条件风险措施，并展示它们如何有助于在许多实际应用中改进操作决策。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，以识别级联故障并减少潜在影响。同时，本项目将为相关研究课题的本科和研究生课程提供新的教材。未被充分代表的博士生将被激励参与研究和教育活动。本项目旨在探索一类条件风险度量，它概括了包括条件风险值在内的许多经典风险度量。由于商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具有挑战性。本项目将探索数据驱动环境下的重新表述和近似方法。更具体地说，将探讨条件风险度量的分布鲁棒版本及其在各种分布模糊设置下的重新表述，将研究基于可用历史数据的条件风险度量的样本近似值，并制定处理条件风险度量的有效解决算法。这个项目的成功完成将为随机优化文献带来新的知识，包括函数优化分析、历史数据的价值、随机整数规划的切割平面。

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 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.