LUNDBERG BOUNDS ON THE TAILS OF COMPOUND DISTRIBUTIONS

Exponential bounds are derived for the tail probabilities of various c ompound distributions generalizing the classical Lundberg inequality o f insurance risk theory. Failure rate properties of the compounding di stribution including log-convexity and log-concavity are considered in some detail. Mixed Poisson compounding distributions are also conside red. A ruin theoretic generalization of the Lundberg inequality is obt ained in the case where the number of claims process is a mixed Poisso n process. An application to the M/G/1 queue length distribution is gi ven.