Asymptotic behavior for sum ruin probability of generalized bidimensional risk model with heavy-tailed claims

This paper considers a generalized bidimensional continuous-time risk model with subexponential claims, constant force of interest and Brownian perturbations, where the claim sizes from each line of business are dependent according to some dependence structure and the two components of each claim-inter-arrival-time vector are arbitrarily dependent. Some asymptotic presentations are shown for the finite-time sum ruin probability defined as the probability that the sum of two surplus processes generated by two lines of business goes below zero over a time horizon [0,t]. Particularly, the claim-number processes from different lines of business can be arbitrarily dependent when the claim sizes are long-tailed and dominatedly-varying-tailed.