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

该项目的目标是发展理论上健全的框架，用于管理离散决策问题中的风险和不确定性。最近在风险管理和分析领域取得的进展，使得能够对复杂的大规模系统中的不确定性进行稳健和有效的控制。这一进展主要是在金融应用范围内取得的，建立了新类型的风险措施。发展的理论和算法框架的条件风险价值的措施和理论的偏差措施构成了原始贡献的PI在这一领域。在这些领域中，现代风险理论的思想和方法尚未广泛建立，但毫无疑问，将大大有助于决策和政策的整体稳健性，例如供应链管理，电信，反恐应用等快速增长的领域，仅举几例。在这些领域的主导模式基本上是离散的性质，并拥有一系列的功能，没有得到适当的反映在当前国家的最先进的风险理论，但在这些问题的风险和不确定性的充分处理是至关重要的。这项研究工作的最终目标是开发新的风险模型和算法，这将有利于使用先进的风险管理技术在广泛的离散决策问题下的不确定性。特别是，它计划采用专门构造的竞争型连贯措施和偏差措施的风险模型的离散优化问题的发展。具体应用领域将包括电信和供应链网络。

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.