Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims

In this paper, a two-dimensional renewal risk model of insurance business with some strongly subexponential claim sizes is considered. Three types of the finite-time ruin probabilities under this model are discussed. We obtain the asymptotic upper and lower bounds for one type, and the asymptotic formulas for the others, which hold uniformly in a corresponding region, respectively.