Uniform asymptotics for the finite-time and infinite-time ruin probabilities in a dependent risk model with constant interest rate and heavy-tailed claims

Abstract

We consider a nonstandard risk model with constant interest rate. For the case where the claim sizes follow a common heavy-tailed distribution and fulfill a dependence structure proposed by Geluk and Tang [J. Geluk and Q. Tang, Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theor. Probab., 22:871–882, 2009] while the interarrival times fulfill the so-called widely lower orthant dependence, we establish a weakly asymptotically equivalent formula for the infinite-time ruin probability. In particular, when the dependence structure for claim sizes is strengthened to the widely upper orthant dependence, this result implies a uniformly asymptotically equivalent formula for the finite-time and infinite-time ruin probabilities.