Uniformly asymptotic behavior of ruin probabilities in a time-dependent renewal risk model with stochastic return

In this paper, we consider a time-dependent risk model, where an insurance company is allowed to invest its wealth in financial assets and the price process of the investment portfolio is described as a geometric Lévy process. When claim sizes have dominatedly varying tails, we obtain some asymptotic formulae for ruin probabilities holding uniformly for some finite or infinite time horizons. We further perform some simulations to check the accuracy of our formulae.