Asymptotic behavior of product of two heavy-tailed dependent random variables

Let X and Y be positive weakly negatively dependent (WND) random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F.(x) = 1.F(x) and G.(x) = 1.G(x) are provided. Moreover, subexponentiality of XY when X and Y are WND random variables is derived.