Parisian ruin probability for spectrally negative Lévy processes

By Ronnie Loeffen, Irmina Czarna, Zbigniew Palmowski. 2011

111 citations recorded by the source corpus.

In this note we give, for a spectrally negative Levy 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 Levy process and the distribution of the process at time r.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/788d46e74b184970f7e0d9ad452e95107b4a69ec

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Zbigniew Palmowski
2. Irmina Czarna
3. Lothar Breuer

In Management Science and Operations Research

1. Zbigniew Palmowski
2. Irmina Czarna
3. Andreas E. Kyprianou
4. Ronnie Loeffen
5. Lothar Breuer
6. Jevgenijs Ivanovs

In Statistics and Probability

1. Zbigniew Palmowski
2. Andreas E. Kyprianou

Citations in the corpus

• An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “2 of Loeffen et al. (2013) which is quite explicit in the context of the present risk model: if κr = inf {t > r : t − gt > r} , where gt = sup {0 ≤ s ≤ t : Xs ≥ 0}, then Px {κr < ∞} = 1 − ψ ′(0+) ∫∞ 0 zW(x + z)P0 (Xr ∈ dz) ∫∞ 0 zP0 (Xr ∈ dz) , (50)”
• Ruin Probability with Parisian Delay for a Spectrally Negative Lévy Risk Process (2010, background): “Another formula for the Parisian ruin probability was recently also derived in [21].”