Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest, in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent. Under some mild conditions, we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval. If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed, it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.