Asymptotic ruin probabilities for a bidimensional renewal risk model

Abstract

This paper studies a bidimensional renewal risk model with constant force of interest and heavy-tailed claims. We extend the existing models through allowing arbitrary dependences between each pair of inter-arrival times of the two kinds of insurance claims. A precise asymptotic formula for the finite-time ruin probability is obtained when the claims have subexponential tails. Further restricting the claim-size distributions within the class of extended regular variation, we derive the corresponding asymptotic formula for the infinite-time ruin probability.