General tax structures and the Lévy insurance risk model
ANDREAS E. KYPRIANOU and XIAOWEN ZHOU
Source: J. Appl. Probab. Volume 46, Number 4
(2009), 1146-1156.
Abstract
In the spirit of Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) we consider a Lévy insurance risk model with tax payments of a more general structure than in the aforementioned papers, which was also considered in Albrecher, Borst, Boxma, and Resing (2009). In terms of scale functions, we establish three fundamental identities of interest which have stimulated a large volume of actuarial research in recent years. That is to say, the two-sided exit problem, the net present value of tax paid until ruin, as well as a generalized version of the Gerber--Shiu function. The method we appeal to differs from Albrecher and Hipp (2007), and Albrecher, Renaud, and Zhou (2008) in that we appeal predominantly to excursion theory.
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Keywords: Reflected Lévy process; passage problem; integrated exponential Lévy process; insurance risk process; ruin; excursion theory
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1261670694
Digital Object Identifier: doi:10.1239/jap/1261670694
Mathematical Reviews number (MathSciNet): MR2582712
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