Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The ruin problem for L\'evy-driven linear stochastic equations with
  applications to actuarial models with negative risk sums   We study the asymptotic of the ruin probability for a process which is the
solution of linear SDE defined by a pair of independent L\'evy processes. Our
main interest is the model describing the evolution of the capital reserve of
an insurance company selling annuities and investing in a risky asset. Let
$\beta>0$ be the root of the cumulant-generating function $H$ of the increment
of the log price process $V$. We show that the ruin probability admits the
exact asymptotic $Cu^{-\beta}$ as the initial capital $u\to\infty$ assuming
only that the law of $V_T$ is non-arithmetic without any further assumptions on
the price process.

19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ