Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed-form solutions for worst-case law invariant risk measures with
  application to robust portfolio optimization   Worst-case risk measures refer to the calculation of the largest value for
risk measures when only partial information of the underlying distribution is
available. For the popular risk measures such as Value-at-Risk (VaR) and
Conditional Value-at-Risk (CVaR), it is now known that their worst-case
counterparts can be evaluated in closed form when only the first two moments
are known for the underlying distribution. These results are remarkable since
they not only simplify the use of worst-case risk measures but also provide
great insight into the connection between the worst-case risk measures and
existing risk measures. We show in this paper that somewhat surprisingly
similar closed-form solutions also exist for the general class of law invariant
coherent risk measures, which consists of spectral risk measures as special
cases that are arguably the most important extensions of CVaR. We shed light on
the one-to-one correspondence between a worst-case law invariant risk measure
and a worst-case CVaR (and a worst-case VaR), which enables one to carry over
the development of worst-case VaR in the context of portfolio optimization to
the worst-case law invariant risk measures immediately.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg