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1 results

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

  • Part of
  • Hyun Suk Park, Ross Maller
  • Journal:
    Advances in Applied Probability / Volume 40 / Issue 3 / September 2008
    Published online by Cambridge University Press:
    01 July 2016, pp. 716-733
    Print publication:
    September 2008
    • Article
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  • 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.