Modified ruin probability for a Cram\'er-Lundberg model driven by a compound mixed Poisson process

Abstract

We study modified ruin probabilities in a Cram\'er-Lundberg model driven by a compound mixed Poisson process. In the heavy-tailed regime, if the integrated claim-size distribution is subexponential and the upper endpoint of the mixing distribution stays below the net-profit boundary, the modified and classical ruin probabilities are asymptotically equivalent. In the light-tailed regime, we prove a fixed-intensity ratio theorem and obtain both an endpoint-atom result and a sharp endpoint-density asymptotic with an explicit constant.