Abstract: We consider a discrete-time risk model with dependence structures, where the claim-sizes \X_n\_n\geq1 follow a one-sided linear process with independent and identically distributed (i.i.d.) innovations \\varepsilon_n\_n\geq1, and the innovations and financial risks form a sequence of independent and identically distributed copies of a random pair (\varepsilon,Y) with dependent components. When the product \varepsilon Y has a heavy-tailed distribution, we establish some asymptotic estimates of the ruin probabilities in this discrete-time risk model. Finally, we use a Crude Monte Carlo (CMC) simulation to verify our results.