英文标题：
《Conditional cores and conditional convex hulls of random sets》
---
作者：
Emmanuel Lepinette and Ilya Molchanov
---
最新提交年份：
2017
---
英文摘要：
  We define two non-linear operations with random (not necessarily closed) sets in Banach space: the conditional core and the conditional convex hull. While the first is sublinear, the second one is superlinear (in the reverse set inclusion ordering). Furthermore, we introduce the generalised conditional expectation of random closed sets and show that it is sandwiched between the conditional core and the conditional convex hull. The results rely on measurability properties of not necessarily closed random sets considered from the point of view of the families of their selections. Furthermore, we develop analytical tools suitable to handle random convex (not necessarily compact) sets in Banach spaces; these tools are based on considering support functions as functions of random arguments. The paper is motivated by applications to assessing multivariate risks in mathematical finance.
---
中文摘要：
我们在Banach空间中定义了两个随机（不一定闭合）集的非线性运算：条件核和条件凸包。第一个是次线性的，第二个是超线性的（逆集合包含排序）。此外，我们引入了随机闭集的广义条件期望，并证明它夹在条件核和条件凸包之间。结果依赖于从选择族的角度考虑的不一定是闭合随机集的可测性。此外，我们开发了适用于处理Banach空间中随机凸集（不一定是紧集）的分析工具；这些工具基于将支持函数视为随机参数的函数。本文旨在应用数学金融中的多元风险评估。
---
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
--
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
--

---
PDF下载：
-->