Discounted penalty function at Parisian ruin for Lévy insurance risk process

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

    Research output: Contribution to journalArticlepeer-review

    145 Downloads (Pure)

    Abstract

    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
    Volume83
    Early online date6 Nov 2017
    DOIs
    Publication statusPublished - 2017

    Keywords

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

    Fingerprint

    Dive into the research topics of 'Discounted penalty function at Parisian ruin for Lévy insurance risk process'. Together they form a unique fingerprint.

    Cite this