Uniform asymptotics for ruin probabilities of a delayed renewal risk model with one-sided linear dependence and stochastic returns

In this article, we consider a renewal risk model with by-claims, where the price process of the investment portfolio follows an exponential Levy process. We further assume that the main claim is a one-sided linear process and there exists a certain dependence structure between the innovations and by-claims. In the presence of heavy tails, we obtain a series of uniform formulas in finite and infinite intervals. In order to better describe the obtained results, we carry on the numerical simulations.