We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random vectors in Euclidean space. We identify the dual representation of such convex bodies and describe a construction that serves as a building block for all so defined convex bodies. Sublinear expectations are studied in mathematical finance within the theory of risk measures. In this way, tools from mathematical finance yield a whole variety of new geometric constructions.

中文翻译：

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由随机向量的次线性期望生成的凸体

我们展示了凸几何中的许多众所周知的变换（特别是质心体、凸浮体和 Ulam 浮体）是一般构造的特殊实例，依赖于将亚线性期望应用于欧几里德空间中的随机向量。我们确定了这种凸体的对偶表示，并描述了一种构造，它作为所有如此定义的凸体的构建块。在风险度量理论的数学金融中研究了次线性期望。通过这种方式，数学金融工具产生了各种各样的新几何结构。