Discounted penalty function at Parisian ruin for Lévy insurance risk process

R. Loeffen, Z. Palmowski and B.A. Surya

Insurance: Mathematics and Economics, 2018, vol. 83, issue C, 190-197

Abstract: In the setting of a Lévy insurance risk process, we present some results regarding the Parisian ruin problem which concerns the occurrence of an excursion below zero of duration bigger than a given threshold r. First, we give the joint Laplace transform of ruin-time and ruin-position (possibly killed at the first-passage time above a fixed level b), which generalizes known results concerning Parisian ruin. This identity can be used to compute the expected discounted penalty function via Laplace inversion. Second, we obtain the q-potential measure of the process killed at Parisian ruin. The results have semi-explicit expressions in terms of the q-scale function and the distribution of the Lévy process.

Keywords: Lévy process; Parisian ruin; Risk process; Ruin; Resolvent; First-passage time (search for similar items in EconPapers)
JEL-codes: C65 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:83:y:2018:i:c:p:190-197

DOI: 10.1016/j.insmatheco.2017.10.008

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