The infinite-time ruin probability for a bidimensional risk model with dependent geometric Lévy price processes

Abstract

In this paper, we focus on a bidimensional risk model with heavy-tailed claims and geometric L?vy price processes, in which the two claim-number processes generated by the two kinds of business are not necessary to be identical and can be arbitrarily dependent. In this model, the claim size vectors (X1,Y1), (X2,Y2),... are supposed to be independent and identically distributed random vectors, but for i ? 1, each pair (Xi,Yi) follows the strongly asymptotic independence structure. Under the assumption that the claims have consistently varying tails, an asymptotic formula for the infinite-time ruin probability is established, which extends the existing results in the literature to some extent.

On the non-closure under convolution for strong subexponential distributions

“…The following dependence structure was introduced in [40] and it was studied in several paper including [54], [40] and [27]. We give this condition of dependence for non-negative random variables and in case these random variables are not bounded from below, we need another condition, as follows.…”