A note on Parisian ruin under a hybrid observation scheme
A note on Parisian ruin under a hybrid observation scheme
In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. (2018). Under this model, the process is observed at Poisson arrival times whenever the business is financially healthy and it is continuously observed when it goes below 0. The Parisian ruin is then declared when the process stays below zero for a consecutive period of time greater than a fixed delay. We improve the result originally obtained in Li et al. (2018) and we compute other fluctuation identities. All identities are given in terms of second-generation scale functions.
Hybrid observation scheme, Lévy insurance risk processes, Parisian ruin, Second-generation scale functions
147-157
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
1 February 2019
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Lkabous, Mohamed Amine
(2019)
A note on Parisian ruin under a hybrid observation scheme.
Statistics and Probability Letters, 145, .
(doi:10.1016/j.spl.2018.09.013).
Abstract
In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. (2018). Under this model, the process is observed at Poisson arrival times whenever the business is financially healthy and it is continuously observed when it goes below 0. The Parisian ruin is then declared when the process stays below zero for a consecutive period of time greater than a fixed delay. We improve the result originally obtained in Li et al. (2018) and we compute other fluctuation identities. All identities are given in terms of second-generation scale functions.
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More information
Accepted/In Press date: 19 September 2018
e-pub ahead of print date: 26 September 2018
Published date: 1 February 2019
Additional Information:
Funding Information:
Funding in support of this work was provided by the Institut des sciences mathématiques (ISM) and the Faculté des sciences at UQAM (Ph.D. scholarships). The author thanks two anonymous referees for their very helpful comments and suggestions.
Funding Information:
Funding in support of this work was provided by the Institut des sciences mathématiques (ISM) and the Faculté des sciences at UQAM (Ph.D. scholarships). The author thanks two anonymous referees for their very helpful comments and suggestions.
Publisher Copyright:
© 2018 Elsevier B.V.
Keywords:
Hybrid observation scheme, Lévy insurance risk processes, Parisian ruin, Second-generation scale functions
Identifiers
Local EPrints ID: 468192
URI: http://eprints.soton.ac.uk/id/eprint/468192
ISSN: 0167-7152
PURE UUID: 3217eb19-a779-440f-b9ea-23ebc03c60cc
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Date deposited: 04 Aug 2022 16:53
Last modified: 17 Mar 2024 13:03
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