Abstract Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been observed by the intriguing concept of the risk quadrangles, for example. Stochastic dominance is a binary relation for random variables to compare random outcomes. It is demonstrated that the concepts of higher order risk measures and stochastic dominance are equivalent, they can be employed to characterize the other. The paper explores these relations and connects stochastic orders, higher order risk measures and the risk quadrangle. Expectiles are employed to exemplify the relations obtained.

Alois Pichler

Computational Management Science

COMPUTATIONAL MANAGEMENT SCIENCE (CMS) 是一本国际期刊，专注于管理科学的所有计算方面。这些包括计算模型的理论和经验分析；计算统计；约束、无约束、鲁棒、随机和组合优化算法的分析和应用；动态模型，例如动态规划和决策树；用于全局优化、建模、学习和预测的新搜索工具和算法；知识获取的模型和工具。强调计算范式是 CMS 的一个预期特征，将其与更经典的运筹学期刊区分开来。官方引用为：COMPUT MANAG SCI

Computational Management Science (CMS) is an international journal that focuses on all computational aspects of management science. The journal covers theoretical and empirical analyses of computational models, computational statistics, analysis and application of constrained and unconstrained optimization, robust and stochastic optimization, and combinatorial optimization algorithms. It also addresses dynamic models, such as dynamic programming and decision trees, as well as new search tools and algorithms for global optimization, modeling, learning, and prediction, along with models and tools for knowledge acquisition. A key feature of CMS is its emphasis on computational paradigms, distinguishing it from more classical operations research journals.

《计算管理科学》(Computational Management Science) 是一本国际期刊，专注于管理科学领域的所有计算方面。期刊内容涵盖计算模型的理论与实证分析、计算统计、约束与无约束优化、鲁棒性与随机性优化、组合优化算法的分析与应用，以及动态模型（如动态规划和决策树）。此外，期刊还关注用于全局优化、建模、学习和预测的新搜索工具和算法，以及知识获取的模型和工具。强调计算范式是《计算管理科学》的一个显著特征，使其与更传统的运筹学期刊有所区别。

Connection between higher order measures of risk and stochastic dominance

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Journal Info

Category	Quartile
SOCIAL SCIENCES, MATHEMATICAL METHODS	3