Percentile-Based Risk Management Approaches in Discrete Decision-Making Problems

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The objective of this project is development of theoretically sound framework for management of risks and uncertainties in discrete decision-making problems. Recent progress in the area of risk management and analysis allows for robust and efficient control of uncertainties in complex large-scale systems. This progress has been achieved mainly in the scope of financial applications with establishment of new types of risk measures. Development of theoretical and algorithmic framework for the Conditional Value-at-Risk measure and the theory of deviation measures constitutes the original contribution of the PIs in this domain. Among the fields, where the ideas and methodology of modern risk theory are not yet widely established, but, undoubtedly, will contribute dramatically to the overall robustness of decisions and policies, are such fast growing areas as supply-chain management, telecommunications, anti-terrorist applications, to name a few. The dominant models in these areas have essentially discrete nature, and possess an array of features that have not been properly reflected in the current state-of-the-art risk theory, yet are critical for adequate handling of risks and uncertainties in these problems. The ultimate goal of this research effort is to develop new risk models and algorithms that will facilitate the use of advanced risk management techniques in a broad spectrum of discrete decision-making problems under uncertainties. In particular, it is planned to employ specially constructed percentile-type coherent measures and deviation measures for development of risk models for discrete optimization problems. Specific application areas will include telecommunication and supply-chain networks.