英文标题：
《Nonlinear expectations of random sets》
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作者：
Ilya Molchanov and Anja M\\\"uhlemann
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最新提交年份：
2019
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英文摘要：
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. This calls for a separate study of sublinear and superlinear expectations, since a change of sign does not convert one to the other in the set-valued setting. We identify the extremal expectations as those arising from the primal and dual representations of them. Several general construction methods for nonlinear expectations are presented and the corresponding duality representation results are obtained. On the application side, sublinear expectations are naturally related to depth trimming of multivariate samples, while superlinear ones can be used to assess utilities of multiasset portfolios.
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中文摘要：
随机变量的次线性泛函称为次线性期望；它们是无限维线性空间上的凸齐次泛函。我们将这个概念推广到定义在可测集值函数（构成非线性空间）上的集值泛函，等价地，推广到随机闭集上。这就需要对次线性和超线性期望进行单独的研究，因为在集值设置中，符号的变化不会将一个转换为另一个。我们将极值期望确定为它们的原始和对偶表示所产生的期望。给出了非线性期望的几种一般构造方法，并得到了相应的对偶表示结果。在应用方面，次线性预期自然与多变量样本的深度微调相关，而超线性预期可用于评估多资产组合的效用。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Functional Analysis 功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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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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