Asymptotic behavior of finite-time ruin probabilities in a bidimensional compound risk model

Consider a bidimensional compound risk model with stochastic premiums and returns, in which an insurer makes both risk-free and risky investments in two lines of business, and an accident may cause more than one claim. In this model, we allow that the two log-price processes are both real-valued Lévy processes, the claim numbers from the same business line, the two accident arrival processes and the two premium processes from two business lines are, respectively, arbitrarily dependent, and the premium processes are also arbitrarily dependent on all other random sources except the log-price processes. Under the condition that all claims from the same line are pairwise quasi-asymptotically independent and consistently varying-tailed, this paper establishes the asymptotic formulas for two types of finite-time ruin probabilities.