LAUSR

Abstract Let X be a real valued random variable with an unbounded distribution F and let Y be a nonnegative valued random variable with a distribution G. Suppose that X and Y satisfy that holds uniformly for as , where is a positive measurable function. Under the condition that holds for all constant b > 0, this paper proved that for some implied and that for some implied , where H is the distribution of the product XY, and is the right endpoint of G, that is, and when is understood as 0. Furthermore, in a discrete-time risk model in which the net insurance loss and the stochastic discount factor are equipped with a dependence structure, a general asymptotic formula for the finite-time ruin probability is obtained when the net insurance losses follow a common subexponential distribution.