Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic analysis for the ratio of the random sum of squares to the
  square of the random sum with applications to risk measures   Let \{X_1, X_2, ...\} be a sequence of independent and identically
distributed positive random variables of Pareto-type with index \alpha>0 and
let \{N(t); t\geq 0\} be a counting process independent of the X_i's. For any
fixed t\geq 0, define T_{N(t)}:=\frac{X_1^2 + X_2^2 + ... + X_{N(t)}^2} {(X_1 +
X_2 + ... + X_{N(t)})^2} if N(t)\geq 1 and T_{N(t)}:=0 otherwise. We derive
limiting distributions for T_{N(t)} by assuming some convergence properties for
the counting process. This is even achieved when both the numerator and the
denominator defining T_{N(t)} exhibit an erratic behavior
(\mathbb{E}X_1=\infty) or when only the numerator has an erratic behavior
(\mathbb{E}X_1<\infty and \mathbb{E}X_1^2=\infty). Thanks to these results, we
obtain asymptotic properties pertaining to both the sample coefficient of
variation and the sample dispersion.

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs