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General tax Structures and the Lévy Insurance Risk Model

Published online by Cambridge University Press:  14 July 2016

Andreas E. Kyprianou*
Affiliation:
The University of Bath
Xiaowen Zhou*
Affiliation:
Concordia University
*
Postal address: Department of Mathematical Sciences, The University of Bath, Claverton Down, Bath BA2 7AY, UK. Email address: a.kyprianou@bath.ac.uk
∗∗Postal address: Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve Blvd. West, Montreal Quebec, H3G 1M8, Canada. Email address: xzhou@mathstat.concordia.ca
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2009 

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