Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness of Kusuoka Representations   This paper addresses law invariant coherent risk measures and their Kusuoka
representations. By elaborating the existence of a minimal representation we
show that every Kusuoka representation can be reduced to its minimal
representation. Uniqueness -- in a sense specified in the paper -- of the risk
measure's Kusuoka representation is derived from this initial result.
  Further, stochastic order relations are employed to identify the minimal
Kusuoka representation. It is shown that measures in the minimal representation
are extremal with respect to the order relations. The tools are finally
employed to provide the minimal representation for important practical
examples. Although the Kusuoka representation is usually given only for
nonatomic probability spaces, this presentation closes the gap to spaces with
atoms.

5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex