Abstract: This paper considers a discrete-time risk model with compound dependence. The risk-free and risky investments of an insurer lead to arbitrarily dependent stochastic discount factors. The claim-sizes are assumed to follow a one-sided linear process with pairwise asymptotically independent innovations. The innovations and the stochastic discount factors are mutually independent. We assume that innovations are not necessarily identically distributed nonnegative random variables with distributions F_1,F_2,\cdots,F_n. When the average distribution n^-1\tsm_i=1^nF_iis heavy-tailed, we establish some asymptotic estimates for the finite-time ruin probabilities of this discrete time risk model. We demonstrate our obtained results through a crude Monte Carlo simulation.