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A Lévy Insurance Risk Process with Tax

  • Hansjörg Albrecher (a1), Jean-François Renaud (a2) and Xiaowen Zhou (a3)
Abstract

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.

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Copyright
Corresponding author
Postal address: Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria.
∗∗ Email address: hansjoerg.albrecher@oeaw.ac.at
∗∗∗ Email address: jean-francois.renaud@oeaw.ac.at
∗∗∗∗ 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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Supported by the Austrian Science Fund Project P18392.

Supported by an NSERC grant.

Footnotes
References
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[1] Albrecher, H. and Hipp, C. (2007). Lundberg's risk process with tax. Blätter der DGVFM 28, 1328.
[2] Avram, F., Palmowski, Z. and Pistorius, M. R. (2007). On the optimal dividend problem for a spectrally negative Lévy process. Ann. Appl. Prob. 17, 156180.
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[20] Zhou, X. (2007). Exit problems for spectrally negative Lévy processes reflected at either the supremum or the infimum. J. Appl. Prob. 44, 10121030.
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