Power identities for Lévy risk models under taxation and capital injections

Details

Ressource 1Download: BIB_D210A60D8A6D.P001.pdf (400.60 [Ko])
State: Public
Version: author
Serval ID
serval:BIB_D210A60D8A6D
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Power identities for Lévy risk models under taxation and capital injections
Journal
Stochastic Systems
Author(s)
Albrecher H., Ivanovs J.
ISSN
1946-5238
Publication state
Published
Issued date
2014
Peer-reviewed
Oui
Volume
4
Number
1
Pages
157-172
Language
english
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.
Keywords
Spectrally negative Lévy processes, exit problems, collective risk theory, insurance, capital injections, dividends, alternative ruin concepts
Open Access
Yes
Create date
21/01/2014 12:42
Last modification date
20/08/2019 15:52
Usage data