On the longest/shortest negative excursion of a Lévy risk process and related quantities
On the longest/shortest negative excursion of a Lévy risk process and related quantities
In this paper, we analyze some distributions involving the longest and shortest negative excursions of spectrally negative Lévy processes using the binomial expansion approach. More specifically, we study the distributions of such excursions and related quantities such as the joint distribution of the shortest and longest negative excursions and their difference (also known as the range) over a random and infinite horizon time. Our results are applied to address new Parisian ruin problems, stochastic ordering and the number near-maximum distress periods showing the superiority of the binomial expansion approach for such cases.
Lévy risk process, Negative excursions, Parisian ruin, time in the red
Lkabous, M.A.
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Palmowski, Z.
260b9de7-828f-4b48-aa15-bc598ffc5cda
Lkabous, M.A.
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Palmowski, Z.
260b9de7-828f-4b48-aa15-bc598ffc5cda
Lkabous, M.A. and Palmowski, Z.
(2024)
On the longest/shortest negative excursion of a Lévy risk process and related quantities.
Scandinavian Actuarial Journal.
(doi:10.1080/03461238.2024.2424273).
Abstract
In this paper, we analyze some distributions involving the longest and shortest negative excursions of spectrally negative Lévy processes using the binomial expansion approach. More specifically, we study the distributions of such excursions and related quantities such as the joint distribution of the shortest and longest negative excursions and their difference (also known as the range) over a random and infinite horizon time. Our results are applied to address new Parisian ruin problems, stochastic ordering and the number near-maximum distress periods showing the superiority of the binomial expansion approach for such cases.
Text
On the longest shortest negative excursion of a L vy risk process and related quantities
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e-pub ahead of print date: 7 November 2024
Keywords:
Lévy risk process, Negative excursions, Parisian ruin, time in the red
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Local EPrints ID: 498994
URI: http://eprints.soton.ac.uk/id/eprint/498994
ISSN: 0346-1238
PURE UUID: cd9e86c9-e827-4773-bd03-a36bc417ed3a
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Date deposited: 06 Mar 2025 17:41
Last modified: 21 Aug 2025 03:46
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Author:
Z. Palmowski
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