Asymptotic ruin probabilities for a two-dimensional risk model with dependent claims and stochastic return

We consider a continuous-time two-dimensional risk model, in which the claims from the two lines of insurance businesses satisfy an extensive asymptotic independence structure and the stochastic return is driven by a geometric Levy process. Under a mild technical condition regarding the Laplace exponent of the Levy process, we obtain explicit asymptotic expansions for both finite-time and infinite-time ruin probabilities when the claim sizes have regularly varying distributions.