Asymptotic Estimates of Finite-Time Ruin Probabilities with Dependent Risks and CMC Simulations

We consider a discrete-time risk model with dependence structures, where the claim-sizes {X_n}_{ngeq1} follow a one-sided linear process with independent and identically distributed (i.i.d.) innovations ${varepsilon_n}_{ngeq1}$, 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.