Discounted penalty function at Parisian ruin for Lévy insurance risk process

Citation data:

Insurance: Mathematics and Economics, ISSN: 0167-6687

Publication Year:
2017
Captures 4
Readers 4
Social Media 26
Shares, Likes & Comments 26
DOI:
10.1016/j.insmatheco.2017.10.008
Author(s):
R. Loeffen; Z. Palmowski; B. A. Surya
Publisher(s):
Elsevier BV
Tags:
Mathematics; Economics, Econometrics and Finance; Decision Sciences
article description
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.