• heavy tail;
  • one-sided linear process;
  • investment return process;
  • ruin probability;
  • Lévy process;
  • renewal risk model

This paper investigates the ruin probabilities of a renewal risk model with stochastic investment returns and dependent claim sizes. The investment is described as a portfolio of one risk-free asset and one risky asset whose price process is an exponential Lévy process. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed step sizes. When the step-size distribution is heavy tailed, we establish some uniform asymptotic estimates for the ruin probabilities of this renewal risk model. Copyright © 2012 John Wiley & Sons, Ltd.