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General tax Structures and the Lévy Insurance Risk Model

Part of: Special processes Stochastic processes Markov processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Andreas E. Kyprianou  and
Xiaowen Zhou
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.

Keywords

Reflected Lévy processpassage problemintegrated exponential Lévy processinsurance risk processruinexcursion theory

MSC classification

Secondary: 60K05: Renewal theory 60K15: Markov renewal processes, semi-Markov processes 91B30: Risk theory, insurance 60G70: Extreme value theory; extremal processes 60J55: Local time and additive functionals
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 4 , December 2009 , pp. 1146 - 1156
Copyright
Copyright © Applied Probability Trust 2009 

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