Parisian ruin for a refracted Lévy process
Parisian ruin for a refracted Lévy process
In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive premium rate, namely a refracted Lévy process. Our main contribution is a generalization of the result in Loeffen et al. (2013) for the probability of Parisian ruin of a standard Lévy insurance risk process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Despite the more general setup considered here, our main result is as compact and has a similar structure. Examples are provided.
Adaptive premium, Lévy risk models, Parisian ruin, Refracted Lévy process, Scale functions
153-163
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Czarna, Irmina
e4148569-df4b-4a6a-940f-c5121eb34c71
Renaud, Jean François
63a85ea5-143a-4110-99a2-b5e5461c9279
1 May 2017
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Czarna, Irmina
e4148569-df4b-4a6a-940f-c5121eb34c71
Renaud, Jean François
63a85ea5-143a-4110-99a2-b5e5461c9279
Lkabous, Mohamed Amine, Czarna, Irmina and Renaud, Jean François
(2017)
Parisian ruin for a refracted Lévy process.
Insurance: Mathematics and Economics, 74, .
(doi:10.1016/j.insmatheco.2017.03.005).
Abstract
In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive premium rate, namely a refracted Lévy process. Our main contribution is a generalization of the result in Loeffen et al. (2013) for the probability of Parisian ruin of a standard Lévy insurance risk process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Despite the more general setup considered here, our main result is as compact and has a similar structure. Examples are provided.
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e-pub ahead of print date: 4 April 2017
Published date: 1 May 2017
Additional Information:
Funding Information:
Irmina Czarna is supported by National Science Centre Grant No. 2015/19/D/ST1/01182.
Publisher Copyright:
© 2017 Elsevier B.V.
Keywords:
Adaptive premium, Lévy risk models, Parisian ruin, Refracted Lévy process, Scale functions
Identifiers
Local EPrints ID: 470529
URI: http://eprints.soton.ac.uk/id/eprint/470529
ISSN: 0167-6687
PURE UUID: c9002cca-38f5-4277-b864-b69edfb7593b
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Date deposited: 12 Oct 2022 16:43
Last modified: 17 Mar 2024 13:03
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Author:
Irmina Czarna
Author:
Jean François Renaud
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