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A Lévy Insurance Risk Process with Tax

Part of: Stochastic processes Markov processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Hansjörg Albrecher ,
Jean-François Renaud  and
Xiaowen Zhou
Hansjörg Albrecher*
Affiliation:
Austrian Academy of Sciences and University of Linz
Jean-François Renaud*
Affiliation:
Austrian Academy of Sciences
Xiaowen Zhou*
Affiliation:
Concordia University
*
∗Postal address: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria.
∗Postal address: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria.
∗∗∗∗Postal address: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd W., Montréal, Québec, H3G 1M8, Canada. Email address: xzhou@mathstat.concordia.ca
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Abstract

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Using fluctuation theory, we solve the two-sided exit problem and identify the ruin probability for a general spectrally negative Lévy risk process with tax payments of a loss-carry-forward type. We study arbitrary moments of the discounted total amount of tax payments and determine the surplus level to start taxation which maximises the expected discounted aggregate income for the tax authority in this model. The results considerably generalise those for the Cramér-Lundberg risk model with tax.

Keywords

Lévy processfluctuation theoryexcursion theoryscale functionsinsurance risk theoryruin probabilitytax payments

MSC classification

Secondary: 60G51: Processes with independent increments; L'evy processes 91B30: Risk theory, insurance 60J75: Jump processes
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 363 - 375
Copyright
Copyright © Applied Probability Trust 2008 

Footnotes

Supported by the Austrian Science Fund Project P18392.

Supported by an NSERC grant.

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