Journal of Applied Probability

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

Erik J. Baurdoux, Juan Carlos Pardo, José Luis Pérez, and Jean-François Renaud

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Abstract

Inspired by the works of Landriault et al. (2011), (2014), we study the Gerber–Shiu distribution at Parisian ruin with exponential implementation delays for a spectrally negative Lévy 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 Lévy processes and relies on the theory of so-called scale functions. In particular, we extend the recent results of Landriault et al. (2011), (2014).

Article information

Source
J. Appl. Probab., Volume 53, Number 2 (2016), 572-584.

Dates
First available in Project Euclid: 17 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1466172875

Mathematical Reviews number (MathSciNet)
MR3514299

Zentralblatt MATH identifier
1344.60046

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 60J99: None of the above, but in this section

Keywords
Scale function Parisian ruin Lévy process excursion theory fluctuation theory Gerber–Shiu function Laplace transform

Citation

Baurdoux, Erik J.; Pardo, Juan Carlos; Pérez, José Luis; Renaud, Jean-François. Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes. J. Appl. Probab. 53 (2016), no. 2, 572--584. https://projecteuclid.org/euclid.jap/1466172875


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