The infinite-time ruin probability for a bidimensional risk model with dependent geometric L\'{e}vy price processes

Abstract

In this paper, we focus on a bidimensional risk model with heavy-tailed claims and geometric L\'{e}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 $\left(X_{1},Y_{1}\right),\left(X_{2},Y_{2}\right),\cdots$ are supposed to be independent and identically distributed random vectors, but each pair $\left(X_{i},Y_{i}\right)$ 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.