AMC-SS: Collaborative Research: Dynamic Stochastic Optimization with Stochastic Ordering Constraints and Risk Functionals

该研究旨在建立风险规避下动态随机系统优化的数学基础。 我们的目标是开发出能够捕捉结果的整个分布的方法，包括小概率但高后果的事件，而不仅仅是平均表现。 风险规避将以两种互补的方式进行建模。 第一种方法是基于随机订单比较系统的随机结果的一些基准结果。 这两种结果都被认为是时间的随机函数。 第二种方法是基于使用的动态风险量化器的质量评估的控制政策的系统。 对于这两类模型，我们将分析由此产生的优化问题，开发最优性条件，并提出寻找最优风险规避策略的方法。 随机最优控制的现有技术解决了系统的平均性能，并且不足以分析和解决其中具有低概率的事件可能是关键的问题。 该项目将提供新的数学工具和数值方法来形式化和解决此类控制问题。 研究结果将适用于医学，军事问题，供应链管理，计算机科学，电信，保险和金融，以及许多其他涉及大量不确定性和风险的领域。

The proposed research aims at building mathematical foundations of optimization of dynamic stochastic systems under risk aversion. Our goal is to develop approaches which will capture the entire distribution of outcomes, including events of small probability but high consequences, rather than just the average performance. Risk aversion will be modeled in two complementary ways. The first approach is based on stochastic orders comparing the random outcomes of the system to some benchmark outcomes. Both outcomes are considered as random functions of time. The second approach is based on the use of dynamic risk quantifiers in the assessment of the quality of the control policy of the system. For both classes of models we shall analyze the resulting optimization problems, develop conditions of optimality, and propose methods for finding optimal risk-averse strategies.The research is motivated by the need to address dynamic decision problems involving risk. The existing techniques of stochastic optimal control address the average performance of the system and are not sufficient to analyze and solve problems in which events with low probability may be crucial. The project will provide new mathematical tools and numerical methods to formalize and solve such control problems. The results of the research will be applicable to medicine, military problems, supply-chain management, computer science, telecommunication, insurance, and finance, and many other areas involving substantial uncertainty and risk.