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摘要翻译：
随机优化问题的目标往往包含期望。当风险也包含在问题描述中时，除了量化可接受的风险外，还必须涉及风险度量，通常是在目标中。为此目的，有一个调整、适应和有效的风险度量评估方案是很重要的。本文阐述了一类重要的风险测度--谱风险测度的不同表示形式。结果使问题的公式简洁，它们特别适用于随机优化问题。基于这些新的结果可以建立有效的评估算法，最终使涉及光谱风险测度的优化问题符合随机优化的条件。
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英文标题：
《Spectral Risk Measures, With Adaptions For Stochastic Optimization》
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作者：
Alois Pichler
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最新提交年份：
2012
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/1209.3570
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