Preprint A21/2006
Translative Sets and Functions and their Applications to Risk Measure Theory and Nonlinear Separation

Andreas Hamel

**Keywords: **
nonlinear separation | coherent risk measure | isotonic Banach functional | topical function | set-valued convex function | translative function

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.