Risk and Reliability in Stochastic Optimisation and Equilibrium

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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.