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2014 Power identities for Lévy risk models under taxation and capital injections
Hansjörg Albrecher, Jevgenijs Ivanovs
Stoch. Syst. 4(1): 157-172 (2014). DOI: 10.1214/12-SSY079

Abstract

In this paper we study a spectrally negative Lévy process which is refracted at its running maximum and at the same time reflected from below at a certain level. Such a process can for instance be used to model an insurance surplus process subject to tax payments according to a loss-carry-forward scheme together with the flow of minimal capital injections required to keep the surplus process non-negative. We characterize the first passage time over an arbitrary level and the cumulative amount of injected capital up to this time by their joint Laplace transform, and show that it satisfies a simple power relation to the case without refraction, generalizing results by Albrecher and Hipp (2007) and Albrecher, Renaud and Zhou (2008). It turns out that this identity can also be extended to a certain type of refraction from below. The net present value of tax collected before the cumulative injected capital exceeds a certain amount is determined, and a numerical illustration is provided.

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Hansjörg Albrecher. Jevgenijs Ivanovs. "Power identities for Lévy risk models under taxation and capital injections." Stoch. Syst. 4 (1) 157 - 172, 2014. https://doi.org/10.1214/12-SSY079

Information

Published: 2014
First available in Project Euclid: 18 September 2014

zbMATH: 1300.60067
MathSciNet: MR3353216
Digital Object Identifier: 10.1214/12-SSY079

Subjects:
Primary: 60G51
Secondary: 60K25

Rights: Copyright © 2014 INFORMS Applied Probability Society

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Vol.4 • No. 1 • 2014
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