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Stochastic Optimization with Certainty Equivalent Measures of Risk

Dr. Pavlo Krokhmal
Donald E. Bently Faculty Fellow and Associate Professor of Industrial Engineering and
Applied Mathematical and Computational Sciences Programs
University of Iowa
April 24, 2015, 2:30 – 3:30 PM
410 John D. Tickle Engineering Building

Dr. Pavlo Krokhmal is a Donald E. Bently Faculty Fellow of Engineering and an Associate Professor of Industrial Engineering and Applied Mathematical and Computational Sciences programs at the University of Iowa. He holds PhD degrees in Operations Research from the University of Florida and in Mechanics and Applied Mathematics from Kyiv University, Ukraine. His research interests include stochastic optimization and risk analysis, probabilistic combinatorial optimization, cooperative control and multi-agent decision making under uncertainty, and data mining. His research in decision making and optimization under uncertainty has been supported by the NSF, the Air Force Office of Scientific Research, Defense Threat Reduction Agency, the Air Force Research Lab, and he is a recipient of the AFOSR Young Investigator Award, National Research Council Senior Research Associateship Award, and several AFOSR Air Force Summer Faculty Fellowship Awards. He is a Co-Editor-in-Chief of Optimization Letters.

Abstract: In this talk we discuss risk-averse decision making and optimization in the presence of uncertainties, when the risks are quantified via a class of statistical functionals known as coherent or convex measures of risk. In particular, we present the family of certainty equivalent measures of risk, which are shown to possess a number of important methodological properties, including consistency with the expected utility theory and second-order stochastic dominance, and are amenable to efficient incorporation in mathematical programming problems. The certainty equivalent risk measures contain, as special cases, the higher moment coherent risk measures and log-exponential convex risk measures, which quantify the risk via higher tail moments of loss distributions, and are particularly useful in problems with “heavy-tailed” distributions. Implementation of certainty equivalent measures of risk in mathematical programming problems introduces specific problem structure, which we explore in developing specialized solution algorithms, such as scenario decomposition and polyhedral approximation methods. A number of case studies, including portfolio optimization, renewable energy grid management, flood insurance, etc., illustrate the developed risk management tools and their performance in real-life problems.

 

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