Ruin probabilities in perturbed risk models

We consider the asymptotical behaviour of the ruin function in perturbed and unperturbed non-standard risk models when the initial risk reserve tends to infinity. We give a characterization of this behaviour in terms of the unperturbed ruin function and the perturbation law provided that at least one of both is subexponential. By a number of examples for the claim arrival process as well as the perturbation process we show that our result is a generalization of previous work on this subject.