On the area in the red of Levy risk processes and related quantities
On the area in the red of Levy risk processes and related quantities
Under contemporary insurance regulatory frameworks, an insolvent insurer placed in receivership may have the option of rehabilitation, during which a plan is devised to resolve the insurer's difficulties. The regulator and receiver must analyze the company's financial condition and determine whether a rehabilitation is likely to be successful or if its problems are so severe that the appropriate action is to liquidate the insurer. Therefore, it is essential to evaluate the cost required to support the insurer during its insolvent states in the decision-making process. To this end, we study areas in the red (below level 0) up to the recovery time, Poissonian, and continuous first passage times in this paper. Furthermore, we extend the study to the areas associated with Parisian ruin to evaluate the total cost until possible liquidation. For spectrally negative Lévy processes (SNLPs), also known as Lévy risk models, we derive the expectations of these quantities in terms of the well-known scale functions. Our results improve the existing literature, in which only expected areas for the Brownian motion and the Cramér-Lundberg risk process with exponential jumps are known.
Area in the red, Cost of recovery, Lévy risk processes
257-278
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Wang, Zijia
8650a4bc-d0db-44c2-a4e9-3ef3f182edb5
29 May 2023
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Wang, Zijia
8650a4bc-d0db-44c2-a4e9-3ef3f182edb5
Lkabous, Mohamed Amine and Wang, Zijia
(2023)
On the area in the red of Levy risk processes and related quantities.
Insurance: Mathematics and Economics, 111, .
(doi:10.1016/j.insmatheco.2023.05.005).
Abstract
Under contemporary insurance regulatory frameworks, an insolvent insurer placed in receivership may have the option of rehabilitation, during which a plan is devised to resolve the insurer's difficulties. The regulator and receiver must analyze the company's financial condition and determine whether a rehabilitation is likely to be successful or if its problems are so severe that the appropriate action is to liquidate the insurer. Therefore, it is essential to evaluate the cost required to support the insurer during its insolvent states in the decision-making process. To this end, we study areas in the red (below level 0) up to the recovery time, Poissonian, and continuous first passage times in this paper. Furthermore, we extend the study to the areas associated with Parisian ruin to evaluate the total cost until possible liquidation. For spectrally negative Lévy processes (SNLPs), also known as Lévy risk models, we derive the expectations of these quantities in terms of the well-known scale functions. Our results improve the existing literature, in which only expected areas for the Brownian motion and the Cramér-Lundberg risk process with exponential jumps are known.
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On the area in the red of Lévy risk processes and related quantities
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Accepted/In Press date: 15 May 2023
e-pub ahead of print date: 19 May 2023
Published date: 29 May 2023
Additional Information:
Funding Information:
We sincerely thank the Handling Editor and two anonymous referees for constructive comments which improve the quality of this paper. Mohamed Amine Lkabous acknowledges the support from a start-up grant from the University of Southampton . Zijia Wang acknowledges the support from a start-up grant from the Chinese University of Hong Kong Business School .
Publisher Copyright:
© 2023 Elsevier B.V.
Keywords:
Area in the red, Cost of recovery, Lévy risk processes
Identifiers
Local EPrints ID: 482848
URI: http://eprints.soton.ac.uk/id/eprint/482848
ISSN: 0167-6687
PURE UUID: 414e9e36-7998-49fb-b031-fc03eacd1127
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Date deposited: 13 Oct 2023 16:47
Last modified: 17 Mar 2024 13:22
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Author:
Zijia Wang
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