On asymptotic ruin probability for a bidimensional renewal risk model with dependent and subexponential main claims and delayed claims

In this paper, we consider a bidimensional renewal risk model with dependent main claims and delayed claims. Concretely, suppose that an insurance company simultaneously operates two kinds of businesses which separately trigger two types of claims named main claims and delayed claims, respectively, the two lines of businesses share a common claim-arrival counting process, and the random pairs from the two main claims as well as the random pairs from the two delayed claims, independent of each other, follow bivariate Farlie–Gumbel–Morgenstern distributions with different parameters. Assuming that all the claims are subexponential, an asymptotic formula of finite-time ruin probability for such a model is derived as the initial surpluses tend to infinity, which extends some recent ones in the literature.