Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Computation of Multivariate Scenario Sets for the Skew-t and
  Generalized Hyperbolic Families   We examine the problem of computing multivariate scenarios sets for skewed
distributions. Our interest is motivated by the potential use of such sets in
the "stress testing" of insurance companies and banks whose solvency is
dependent on changes in a set of financial "risk factors". We define
multivariate scenario sets based on the notion of half-space depth (HD) and
also introduce the notion of expectile depth (ED) where half-spaces are defined
by expectiles rather than quantiles. We then use the HD and ED functions to
define convex scenario sets that generalize the concepts of quantile and
expectile to higher dimensions. In the case of elliptical distributions these
sets coincide with the regions encompassed by the contours of the density
function. In the context of multivariate skewed distributions, the equivalence
of depth contours and density contours does not hold in general. We consider
two parametric families that account for skewness and heavy tails: the
generalized hyperbolic and the skew-t distributions. By making use of a
canonical form representation, where skewness is completely absorbed by one
component, we show that the HD contours of these distributions are
"near-elliptical" and, in the case of the skew-Cauchy distribution, we prove
that the HD contours are exactly elliptical. We propose a measure of
multivariate skewness as a deviation from angular symmetry and show that it can
explain the quality of the elliptical approximation for the HD contours.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn