Shock Models Driven by a Cluster Process with Lévy Perturbation and their Applications in Insurance Risk

We construct a class of new cumulative and extreme shock models based on cluster point processes with insurance risk background. For describing the randomicity of environment, a perturbation process is also incorporated into our models. Under the basic assumptions that the primary shock process is a non-homogeneous Poisson and the perturbing term is a Lévy process, we investigate the asymptotic behaviors of the reliability system and applied the corresponding results to non-life insurance risk issue.