标题： 谱风险度量，针对随机优化的适应性 显示英文标题

标题： Spectral Risk Measures, With Adaptions For Stochastic Optimization

摘要： 随机优化问题通常在其目标函数中涉及期望。当风险也被纳入问题描述时，则需要引入风险度量来量化可接受的风险，通常是在目标函数中。为此，拥有一个经过调整、适应且高效的用于评估风险度量的方案非常重要。本文详细阐述了一类重要的风险度量——光谱风险度量的不同表示形式。这些结果允许简洁的问题表述，尤其适合于随机优化问题。基于这些新成果可以构建高效的评估算法，最终使得涉及光谱风险度量的优化问题能够适用于随机优化。 显示英文摘要

摘要： Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. For this purpose it is important to have an adjusted, adapted and efficient evaluation scheme for the risk measure available. In this article different representations of an important class of risk measures, the spectral risk measures, are elaborated. The results allow concise problem formulations, they are particularly adapted for stochastic optimization problems. Efficient evaluation algorithms can be built on these new results, which finally make optimization problems involving spectral risk measures eligible for stochastic optimization.