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.
