The finite-time ruin probability with heavy-tailed and dependent insurance and financial risks

Consider a discrete-time insurance risk model in which the insurer makes both risk-free and risky investments. Assume that the one-period insurance and financial risks form a sequence of independent and identically distributed copies of a random pair (X,Y) with dependent components. When the product XY is heavy tailed, under a mild restriction on the dependence structure of (X,Y), we establish for the finite-time ruin probability an asymptotic formula, which coincides with the long-standing one in the literature. Various important special cases are presented, showing that our work generalizes and unifies some of recent ones.