Power identities for Lévy risk models under taxation and capital injections

Détails

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Etat: Public
Version: de l'auteur
ID Serval
serval:BIB_D210A60D8A6D
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Power identities for Lévy risk models under taxation and capital injections
Périodique
Stochastic Systems
Auteur(s)
Albrecher H., Ivanovs J.
ISSN
1946-5238
Statut éditorial
Publié
Date de publication
2014
Peer-reviewed
Oui
Volume
4
Numéro
1
Pages
157-172
Langue
anglais
Résumé
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.
Mots-clé
Spectrally negative Lévy processes, exit problems, collective risk theory, insurance, capital injections, dividends, alternative ruin concepts
Open Access
Oui
Création de la notice
21/01/2014 12:42
Dernière modification de la notice
20/08/2019 15:52
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