论文标题
在有条件的奇西尼的手段和风险措施上
On Conditional Chisini Means and Risk Measures
论文作者
论文摘要
给定有界随机变量空间上的实际有价值的函数t，我们研究了存在条件版本的非线性均值的问题。我们遵循Chisini（1929）的开创性思想，将平均值定义为T的均值解决方案。我们提供了足够的条件，可以保证存在无限多个功能方程系统的（唯一）解决方案，这将提供所谓的条件性chisini均值。我们将发现应用于表征有条件风险度量的标量，这是Detlefsen和Scandolo（2005）最初采用的必不可少的工具，以推断出强大的双重表示。
Given a real valued functional T on the space of bounded random variables, we investigate the problem of the existence of a conditional version of nonlinear means. We follow a seminal idea by Chisini (1929), defining a mean as the solution of a functional equation induced by T. We provide sufficient conditions which guarantee the existence of a (unique) solution of a system of infinitely many functional equations, which will provide the so called Conditional Chisini mean. We apply our findings in characterizing the scalarization of conditional Risk Measures, an essential tool originally adopted by Detlefsen and Scandolo (2005) to deduce the robust dual representation.
