Uniform asymptotics for ruin probabilities in a dependent renewal risk model with stochastic return on investments

In this paper, an insurer is allowed to make risk-free and risky investments, and the price process of the investment portfolio is described as an exponential Lévy process. We study the asymptotic tail behavior for a non-standard renewal risk model with dependence structures. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed step sizes, and the step sizes and inter-arrival times form a sequence of independent and identically distributed random pairs with a dependence structure. When the step-size distribution is heavy tailed, we obtain some uniform asymptotics for the finite-and infinite-time ruin probabilities.