 Bridging the first and last passage times for Lévy modelsDavid Landriault, Bin Li, Mohamed Amine Lkabous and Zijia Wang Stochastic Processes and their Applications, 2023, vol. 157, issue C, 308-334 Abstract: Research in classical ruin theory has largely focused on the first passage time analysis of a surplus process below level 0. Recently, inspired by numerous applications in finance, physics, and optimization, there has been an accrued interest in the analysis of the last passage time (below level 0). In this paper, we aim to bridge the first and the last passage times and unify their analyses. For this purpose, we consider negative excursions of an underlying process in two manners, cumulative and noncumulative, and introduce two random times, denoted by sr and lr, where r can be interpreted as a measure of a decision maker’s tolerance to negative excursions. Our analysis focuses on spectrally negative Lévy processes, for which we derive the Laplace transform and some distributional quantities of these random times in terms of standard scale functions. An application to credit risk management is considered at the end. Keywords: First passage time; Last passage time; Occupation time; Parisian time; Spectrally negative Lévy processes; Scale functions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:157:y:2023:i:c:p:308-334 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.12.005 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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