Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random recurrence equations and ruin in a Markov-dependent stochastic
  economic environment   We develop sharp large deviation asymptotics for the probability of ruin in a
Markov-dependent stochastic economic environment and study the extremes for
some related Markovian processes which arise in financial and insurance
mathematics, related to perpetuities and the $\operatorname {ARCH}(1)$ and
$\operatorname {GARCH}(1,1)$ time series models. Our results build upon work of
Goldie [Ann. Appl. Probab. 1 (1991) 126--166], who has developed tail
asymptotics applicable for independent sequences of random variables subject to
a random recurrence equation. In contrast, we adopt a general approach based on
the theory of Harris recurrent Markov chains and the associated theory of
nonnegative operators, and meanwhile develop certain recurrence properties for
these operators under a nonstandard "G\"artner--Ellis" assumption on the
driving process.

8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex