Uncertainty is prevalent in engineering design, statistical learning, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative optimization models expressed using measures of risk and related concepts. We survey the rapid development of risk measures over the last quarter century. From their beginning in financial engineering, we recount the spread to nearly all areas of engineering and applied mathematics. Solidly rooted in convex analysis, risk measures furnish a general framework for handling uncertainty with significant computational and theoretical advantages. We describe the key facts, list several concrete algorithms, and provide an extensive list of references for further reading. The survey recalls connections with utility theory and distributionally robust optimization, points to emerging applications areas such as fair machine learning, and defines measures of reliability.

翻译：不确定性广泛存在于工程设计、统计学习及一般性决策过程中。由于固有的风险规避倾向以及对假设条件的模糊性，通常通过构建并求解以风险测度及相关概念表达的保守优化模型来应对不确定性。本文综述了过去二十五年间风险测度的快速发展历程。从金融工程领域的起源出发，我们梳理了其向几乎所有工程与应用数学领域的扩展。基于凸分析的坚实理论根基，风险测度为处理不确定性提供了具有显著计算优势与理论优势的通用框架。我们阐述了关键定理，列举了若干具体算法，并提供了详尽的参考文献以利进一步研读。本综述回溯了其与效用理论及分布鲁棒优化的内在联系，指出了公平机器学习等新兴应用领域，并定义了可靠性测度。