Upper bounds for ruin probabilities in two dependent risk models under rates of interest

In this article, we consider two discrete‐time risk models, in which dependent structures of the payments and the interest force are considered. Two autoregressive moving‐average (ARMA) models are introduced to model the premiums and rates of interest, and the claims are assumed to be independent. Generalized Lundberg inequalities for the ruin probabilities are derived by using renewal recursive technique, which extend some known results. Copyright © 2009 John Wiley & Sons, Ltd.