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June 2016 Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes
Erik J. Baurdoux, Juan Carlos Pardo, José Luis Pérez, Jean-François Renaud
Author Affiliations +
J. Appl. Probab. 53(2): 572-584 (June 2016).

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).

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Erik J. Baurdoux. Juan Carlos Pardo. José Luis Pérez. Jean-François Renaud. "Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes." J. Appl. Probab. 53 (2) 572 - 584, June 2016.

Information

Published: June 2016
First available in Project Euclid: 17 June 2016

zbMATH: 1344.60046
MathSciNet: MR3514299

Subjects:
Primary: 60G51
Secondary: 60J99

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 2 • June 2016
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