Translative Sets and Functions and their Applications to Risk Measure Theory and Nonlinear Separation
Translative Sets and Functions and their Applications to Risk Measure Theory and Nonlinear Separation
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发表时间：
2006
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通讯作者：
A. Hamel
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作者：
A. Hamel
最近定义的概念，如Tammer和Weidner提出的非线性分离泛函，Delbaen等人提出的相干风险测度，Gunawardena和Keane提出的局部函数以及等压Banach泛函，都是一致的，可以追溯到1957年Day和1964年Krasnosel’skij的书中。本文给出了这些概念的一般背景，并对集值函数进行了推广。对于一个或有限元素集合的可译性是本注释中集合和函数的关键性质。
Recently defined concepts such as nonlinear separation functionals due to Tammer and Weidner, coherent risk measures due to Delbaen et al., topical functions due to Gunawardena and Keane as well as isotonic Banach functionals coincide and can be traced back to books by Day from 1957 and Krasnosel’skij’s from 1964. This paper is to get out the common background of these concepts and to give an extension to set–valued functions. Translativity with respect to one or a finite collection of elements turns out to be the key property of sets and functions in this note.