Risk and Reliability in Stochastic Optimisation and Equilibrium

这个项目寻求开发优化的理论和方法，利用决策制定中理解和处理风险的最新进展。面对不确定性的优化问题必须面对这样一种内在风险，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，必须做出可靠的决定。最近的理论发展，超越了刚刚预期的值和分位数，提供了取得重大新进展的希望。这个项目的目标不仅是在优化方面取得这样的进步，而且在同样必须处理不确定性的均衡模型方面也是如此。将现有的理论和方法推广到这样的多阶段随机模型是一个挑战。除了接受这一挑战本身，这项研究的一个主要目标将是将结果用于求解算法。

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.