Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models

In this paper, we consider uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional renewal risk models with constant interest forces and diffusion generated by Brownian motions. In one of the models, two classes of claims have different arrival times, while in the another model, two classes of claims share the same arrival times. In both models, two classes of claim sizes are both upper tail asymptotically independent and their distributions belong to the intersection of the long-tailed distribution class and the dominatedly-varying-tailed distribution class, and the inter-arrival times follow a widely lower orthant dependence structure. In each model, we obtain three kinds of uniform asymptotics for the finite-time ruin probabilities, respectively.