Poissonian occupation times of spectrally negative Lévy processes with applications
Poissonian occupation times of spectrally negative Lévy processes with applications
In this paper, we introduce the concept of Poissonian occupation times below level 0 of a spectrally negative Lévy process. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known continuously observed quantities involving occupation times of spectrally negative Lévy processes. As an application, we establish a link between Poissonian occupation times and insurance risk models with Parisian implementation delays.
Lé, Occupation times, Parisian ruin, scale functions, vy insurance risk processes
916-935
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
26 November 2021
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Lkabous, Mohamed Amine
(2021)
Poissonian occupation times of spectrally negative Lévy processes with applications.
Scandinavian Actuarial Journal, 2021 (10), .
(doi:10.1080/03461238.2021.1907783).
Abstract
In this paper, we introduce the concept of Poissonian occupation times below level 0 of a spectrally negative Lévy process. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known continuously observed quantities involving occupation times of spectrally negative Lévy processes. As an application, we establish a link between Poissonian occupation times and insurance risk models with Parisian implementation delays.
Text
Lkabous-14-01-2020
- Accepted Manuscript
More information
Accepted/In Press date: 21 March 2021
e-pub ahead of print date: 28 April 2021
Published date: 26 November 2021
Additional Information:
Funding Information:
The author would like to thank Pr. David Landriault and Pr. Bin Li for the stimulating discussions on the topic.
Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
Keywords:
Lé, Occupation times, Parisian ruin, scale functions, vy insurance risk processes
Identifiers
Local EPrints ID: 449828
URI: http://eprints.soton.ac.uk/id/eprint/449828
ISSN: 0346-1238
PURE UUID: 78af1ff8-e4c7-48a7-aace-8e2893b3c8c5
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Date deposited: 18 Jun 2021 16:31
Last modified: 17 Mar 2024 06:37
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