Asymptotics and uniform asymptotics for finite-time and infinite-time absolute ruin probabilities in a dependent compound renewal risk model

In this paper, we consider a dependent compound renewal risk model with constant premium rate and interest rate, where the individual claim sizes are widely orthant dependent and the claim number has a distribution belonging to the intersection among the maximum domain of attraction of the Gumbel distribution, the subexponential class and the rapidly-varying class. In such a dependent compound renewal (or Poisson) risk model, we obtain the asymptotics and uniform asymptotics for the finite-time and infinite-time absolute ruin probabilities. To this end, we investigate the tail behavior of the random sum with some widely orthant dependent summands and the random number in the maximum domain of attraction of the Gumbel distribution.