Journal of Applied Probability
- J. Appl. Probab.
- Volume 53, Number 2 (2016), 572-584.
Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes
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).
J. Appl. Probab., Volume 53, Number 2 (2016), 572-584.
First available in Project Euclid: 17 June 2016
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 60J99: None of the above, but in this section
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