# Ruin excursions, the $G/G/\infty$ queue and tax payments in renewal risk models

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### Abstract

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/$\infty$ queue and use it to derive some explicit ruin probability formulas. 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.
Original language English Eindhoven Eurandom 15 Published - 2010

### Publication series

Name Report Eurandom 2010039 1389-2355
Name Calculemus : symposium on on the integration of symbolic computtaion and mechanized reasoning : proceedings 14

• ## Cite this

Albrecher, H., Borst, S. C., Boxma, O. J., & Resing, J. A. C. (2010). Ruin excursions, the $G/G/\infty$ queue and tax payments in renewal risk models. (Report Eurandom; Vol. 2010039), (Calculemus : symposium on on the integration of symbolic computtaion and mechanized reasoning : proceedings; Vol. 14). Eurandom.