Finding efficient recursions for risk aggregation by computer algebra

  • Authors:

  • Stefan Gerhold;Richard Warnung

  • Affiliations:

  • Vienna University of Technology, Wiedner Hauptstraíe 8-10, A-1040 Vienna, Austria;Vienna University of Technology, Wiedner Hauptstraíe 8-10, A-1040 Vienna, Austria

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

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Abstract

We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the assumption that the probability generating function of the claim size be algebraic. The probability generating function of the claim number is supposed to be from the rather general class of D-finite functions.