Asymptotics for a multidimensional risk model with a random number of delayed claims and multivariate regularly varying distribution

This paper investigates a continuous-time multidimensional risk model with stochastic returns driven by a geometric Lévy process, where each main claim is accompanied by a random number of delayed claims. By employing a framework of multivariate regular variation for claim sizes and allowing for arbitrarily dependent claim-number processes, we conduct asymptotic analyses for two types of ruin probabilities. Numerical examples are used to demonstrate the accuracy of our asymptotic estimates.