On occupation times in the red of Lévy risk models
On occupation times in the red of Lévy risk models
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum.
Inverse occupation time, Lévy insurance risk processes, Occupation time, Parisian ruin, Scale functions
17-26
Landriault, David
cb59d585-94dd-4a67-a4b1-18a1baeb0505
Li, Bin
b96a645c-851a-4861-b2da-c531001e51d4
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
1 May 2020
Landriault, David
cb59d585-94dd-4a67-a4b1-18a1baeb0505
Li, Bin
b96a645c-851a-4861-b2da-c531001e51d4
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Landriault, David, Li, Bin and Lkabous, Mohamed Amine
(2020)
On occupation times in the red of Lévy risk models.
Insurance: Mathematics and Economics, 92, .
(doi:10.1016/j.insmatheco.2020.02.011).
Abstract
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum.
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More information
Accepted/In Press date: 24 February 2020
e-pub ahead of print date: 28 February 2020
Published date: 1 May 2020
Keywords:
Inverse occupation time, Lévy insurance risk processes, Occupation time, Parisian ruin, Scale functions
Identifiers
Local EPrints ID: 468193
URI: http://eprints.soton.ac.uk/id/eprint/468193
ISSN: 0167-6687
PURE UUID: ed7ba968-f607-4677-8af0-153b09d2276f
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Date deposited: 04 Aug 2022 16:53
Last modified: 17 Mar 2024 13:03
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Author:
David Landriault
Author:
Bin Li
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