Asymptotics for a perturbed bidimensional delay-claim risk model with heavy-tailed claims and stochastic returns

This article considers a bidimensional delay-claim renewal risk model with stochastic returns and Brownian perturbations, in which the main claim and corresponding delayed claim from the same business line are dependent according to a general dependence structure, the price process of stochastic return is described as a geometric Lévy process, and the generic inter-arrival times of the two kinds of main claims are arbitrarily dependent. In the presence of subexponential or the intersection of dominatedly varying tailed and long-tailed main and delayed claims, the corresponding asymptotic formulas for four types of finite-time ruin probabilities are established, and some numerical studies are conducted to verify the accuracy of our asymptotic formulas.