## Journal of Applied Probability

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

#### 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

https://projecteuclid.org/euclid.jap/1324046014

Digital Object Identifier
doi:10.1239/jap/1324046014

Mathematical Reviews number (MathSciNet)
MR2896663

Zentralblatt MATH identifier
1232.60036

#### 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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