Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimization of conditional convex risk measures   Optimization of conditional convex risk measure is a central theme in dynamic
portfolio selection theory, which has not yet systematically studied in the
previous literature perhaps since conditional convex risk measures are neither
random strictly convex nor random coercive. The purpose of this paper is to
give some basic results on the existence and uniqueness on this theme, in
particular our results for conditional monotone mean--variance and conditional
entropic risk measures are complete and deep. As the basis for the work of this
paper, this paper first begins with a brief introduction to random functional
analysis, including the historical backgrounds for its birth and some important
advances. This paper then further surveys some recent progress in random convex
analysis and its applications to conditional convex risk measures. Finally,
based on these, we establish a concise sufficient and necessary condition for a
return to be a solution to the optimization problem of conditional monotone
mean--variance. We also make use of the recently developed theory of
$L^0$--convex compactness to establish the existence of the optimization
problem of conditional entropic risk measure when the conditional mean of
returns is given and the returns fall within a random closed ball. Besides, the
related uniqueness problems are also solved.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol