Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models

In this paper we investigate the number and maximum severity of the ruin excursion of the insurance portfolio reserve process in the Cramér--Lundberg model with and without tax payments. We also provide a relation of the Cramér--Lundberg risk model with the G/G/8 queue and use it to derive some explicit ruin probability formulae. Finally, the renewal risk model with tax is considered, and an asymptotic identity is derived that in some sense extends the tax identity of the Cramér-- Lundberg risk model.