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2 results

  • Lundberg bounds on the tails of compound distributions

  • Part of
  • Gordon E. Willmot, Xiaodong Lin
  • Journal:
    Journal of Applied Probability / Volume 31 / Issue 3 / September 1994
    Published online by Cambridge University Press:
    14 July 2016, pp. 743-756
    Print publication:
    September 1994

  • Exponential bounds are derived for the tail probabilities of various compound distributions, generalizing the classical Lundberg inequality of insurance risk theory. Failure rate properties of the compounding distribution including log-convexity and log-concavity are considered in some detail. Mixed Poisson compounding distributions are also considered. A ruin theoretic generalization of the Lundberg inequality is obtained in the case where the number of claims process is a mixed Poisson process. An application to the M/G/1 queue length distribution is given.