An excursion theoretic approach to Parisian ruin problem
type: Item
instance of: scholarly article
title: An excursion theoretic approach to Parisian ruin problem
zbMATH Open document ID: 1548.91096
author: Bo Li
author: Xiaowen Zhou
published in: Insurance Mathematics \& Economics
publication date: 2024-09-18T00:00:00Z
review text: For a surplus process modelled by \(X\), the Parisian ruin time with duration \(\gamma>0\) is defined as the first time when the process has continuously stayed below \(0\) for a period of length \(\gamma\), i.e. when an excursion below \(0\) of the surplus process has first reached length \(\gamma.\) Applying excursion theory, the authors re-express several well studied fluctuation quantities associated to Parisian ruin for Lévy risk processes in terms of integrals with respect to the corresponding excursion measure. \newline It is shown that these new expressions reconcile with the previous results on the Parisian ruin problem.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 91G05
Mathematics Subject Classification ID: 60G51
zbMATH DE Number: 7915297
zbMATH Keywords: Parisian ruin
zbMATH Keywords: risk process
zbMATH Keywords: excursion theory
zbMATH Keywords: spectrally negative Lévy process
MaRDI profile type: Publication
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DOI: 10.1016/J.INSMATHECO.2024.05.001
description: scientific article; zbMATH DE number 7915297