Asymptotic ruin probabilities for risk processes with dependent increments

In this paper, we derive a Lundberg type result fur asymptotic ruin probabi lities in the case of a risk process with dependent increments. We only ass ume that the probability generating functions exist, and that their logarit hmic average converges. Under these assumptions we present an elementary pr oof of the Lundberg limiting result, which only uses simple exponential ine qualities, and does not rely on results from large deviation theory. Moreov er, we use dependence orderings to investigate, how dependencies between th e claims affect the Lundberg coefficient. The results are illustrated by se veral examples, including Gaussian and AR(1)-processes, and a risk process with adapted premium rules. (C) 2001 Elsevier Science B.V. All rights reser ved.