Ruin probability of renewal risk model with stochastic investment returns and one-sided linear time-dependent claims

Abstract

This paper considers a time-dependent renewal risk model with stochastic investment returns and dependent claim sizes. In the model, the investment returns are described as a geometric Levy process, while the claim sizes are modeled by a one-sided linear process with independent and identically distributed innovations. In addition, the innovations and claim inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, and each pair obeys a dependence structure described via the asymptotic of the conditional tail probability of the innovation given the inter-arrival time. When the innovation distribution is heavy tailed, we derive uniform estimates for ruin probabilities over certain time regions.