In a Cramér-Lundberg model with compound mixed Poisson claims, modified ruin probabilities are asymptotically equivalent to classical ones when the integrated claim-size distribution is subexponential and the mixing distribution's upper endpoint lies below the net-profit boundary; light-tailed cases
Grandell,Mixed Poisson Processes
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Modified ruin probability for a Cram\'er-Lundberg model driven by a compound mixed Poisson process
In a Cramér-Lundberg model with compound mixed Poisson claims, modified ruin probabilities are asymptotically equivalent to classical ones when the integrated claim-size distribution is subexponential and the mixing distribution's upper endpoint lies below the net-profit boundary; light-tailed cases