Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes

Baurdoux, Erik J. ORCID: 0000-0002-5407-0683, Pardo, Juan Carlos, Perez, Jose Luis and Renaud, Jean-Francois (2016) Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes. Journal of Applied Probability, 53 (2). pp. 572-584. ISSN 0021-9002

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Abstract

Inspired by works of Landriault et al. [11, 12], we study the Gerber{Shiu distribution at Parisian ruin with exponential implementation delays for a spectrally negative Levy insurance risk process. To be more specific, we study the so-called Gerber{Shiu distribution for a ruin model where at each time the surplus process goes negative, an independent exponential clock is started. If the clock rings before the surplus becomes positive again then the insurance company is ruined. Our methodology uses excursion theory for spectrally negative Levy processes and relies on the theory of so-called scale functions. In particular, we extend recent results of Landriault et al. [11, 12].

Item Type:	Article
Official URL:	http://projecteuclid.org/current/euclid.jap
Additional Information:	© 2016 Applied Probability Trust
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	18 Dec 2015 12:00
Last Modified:	12 Dec 2024 01:06
Funders:	Natural Sciences and Engineering Research Council of Canada (NSERC), Fonds de recherche du Quebec- Nature et technologies (FRQNT)
URI:	http://eprints.lse.ac.uk/id/eprint/64748

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