Discounted penalty function at Parisian ruin for Lévy insurance risk process

Ronnie Loeffen, Z. Palmowski, B.A. Surya

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    In the setting of a L´evy 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 generalises 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 theq-scale function and the distribution of the L´evy process.
    Original languageEnglish
    Pages (from-to)190-197
    JournalInsurance: Mathematics and Economics
    Early online date6 Nov 2017
    Publication statusPublished - 2017


    • L´evy process
    • Parisian ruin; risk process
    • ruin
    • resolvent
    • first- passage time


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