Journal of Applied Probability

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

Hansjörg Albrecher, Sem C. Borst, Onno J. Boxma, and Jacques Resing

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/∞ 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.

Article information

Source
J. Appl. Probab., Volume 48A (2011), 3-14.

Dates
First available in Project Euclid: 18 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1318940451

Digital Object Identifier
doi:10.1239/jap/1318940451

Mathematical Reviews number (MathSciNet)
MR2865612

Zentralblatt MATH identifier
1223.91024

Subjects
Primary: 91B30: Risk theory, insurance
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]

Keywords
Classical risk model ruin probability G/G/∞ queue tax renewal model

Citation

Albrecher, Hansjörg; Borst, Sem C.; Boxma, Onno J.; Resing, Jacques. Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models. J. Appl. Probab. 48A (2011), 3--14. doi:10.1239/jap/1318940451. https://projecteuclid.org/euclid.jap/1318940451


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