## Bernoulli

• Bernoulli
• Volume 19, Number 2 (2013), 599-609.

### Parisian ruin probability for spectrally negative Lévy processes

#### Abstract

In this note we give, for a spectrally negative Lévy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period $r$. The formula involves only the scale function of the spectrally negative Lévy process and the distribution of the process at time $r$.

#### Article information

Source
Bernoulli Volume 19, Number 2 (2013), 599-609.

Dates
First available in Project Euclid: 13 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1363192039

Digital Object Identifier
doi:10.3150/11-BEJ404

Mathematical Reviews number (MathSciNet)
MR3037165

Zentralblatt MATH identifier
1267.60054

#### Citation

Loeffen, Ronnie; Czarna, Irmina; Palmowski, Zbigniew. Parisian ruin probability for spectrally negative Lévy processes. Bernoulli 19 (2013), no. 2, 599--609. doi:10.3150/11-BEJ404. https://projecteuclid.org/euclid.bj/1363192039.

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