Journal of Applied Probability

Ruin probability with Parisian delay for a spectrally negative Lévy risk process

Irmina Czarna and Zbigniew Palmowski

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Abstract

In this paper we analyze the so-called Parisian ruin probability, which arises when the surplus process stays below 0 longer than a fixed amount of time ζ > 0. We focus on a general spectrally negative Lévy insurance risk process. For this class of processes, we derive an expression for the ruin probability in terms of quantities that can be calculated explicitly in many models. We find its Cramér-type and convolution-equivalent asymptotics when reserves tend to ∞. Finally, we analyze some explicit examples.

Article information

Source
J. Appl. Probab., Volume 48, Number 4 (2011), 984-1002.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046014

Digital Object Identifier
doi:10.1239/jap/1324046014

Mathematical Reviews number (MathSciNet)
MR2896663

Zentralblatt MATH identifier
1232.60036

Subjects
Primary: 60J99: None of the above, but in this section 93E20: Optimal stochastic control 60G51: Processes with independent increments; Lévy processes

Keywords
Lévy process ruin probability asymptotics Parisian ruin risk process

Citation

Czarna, Irmina; Palmowski, Zbigniew. Ruin probability with Parisian delay for a spectrally negative Lévy risk process. J. Appl. Probab. 48 (2011), no. 4, 984--1002. doi:10.1239/jap/1324046014. https://projecteuclid.org/euclid.jap/1324046014


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