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

点击翻译按钮获取中文摘要

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.