Risk and Reliability in Stochastic Optimisation and Equilibrium

该项目旨在发展优化的理论和方法，利用最近在理解和处理决策风险方面的进展。面对不确定性的优化问题必须面对内在的风险，即在知道成本和约束可能依赖的关键随机变量的结果之前，必须做出可靠的决策。最近的理论发展，以超出预期值和分位数的“风险度量”为特征，为重大新进展带来了希望。这个项目的目的是实现这样的进步，不仅在优化，而且在平衡模型，同样必须处理不确定性。将现有的理论和方法扩展到这种多阶段随机模型是一个挑战。除了为了自己的利益而接受这一挑战外，本研究的一个主要目标是将结果用于解决算法。

This project seeks to develop theory and methodology in optimisation which take advantage of recent progress in understanding and treating risk in decision making. Problems of optimisation in the face of uncertainty must confront the risk inherent in having to make reliable decisions before knowing the outcomes of crucial random variables on which costs and constraints may depend. Recent theoretical developments, featuring ‘measures of risk’ beyond just-expected values and quantiles offer hope of major new advances. This project aims to achieve such advances not only in optimisation but also in models of equilibrium that likewise have to deal with uncertainty. Extending current theory and methodology to such multi-stage stochastic models is a challenge. Besides taking up this challenge for its own sake, a major goal of this research will be to use the results in solution algorithms.