Moment and MGF convergence of overshoots and undershoots for Lévy insurance risk processes

Hyun Suk Park*, Ross Maller

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    Abstract

    This paper is concerned with the finiteness and large-time behaviour of moments of the overshoot and undershoot of a high level, and of their moment generating functions (MGFs), for a Lévy process which drifts to-∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process. Results of Klüppelberg, Kyprianou, and Maller (2004) and Doney and Kyprianou (2006) for asymptotic overshoot and undershoot distributions in the class of Lévy processes with convolution equivalent canonical measures are shown to have moment and MGF convergence extensions.

    Original languageEnglish
    Pages (from-to)716-733
    Number of pages18
    JournalAdvances in Applied Probability
    Volume40
    Issue number3
    DOIs
    Publication statusPublished - 2008

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