Improved Analytical Bounds for Some Risk Quantities

Werner Hürlimann

ASTIN Bulletin, 1996, vol. 26, issue 2, 185-199

Abstract: Simple analytical lower and upper bounds are obtained for stop-loss premiums and ruin probabilities of compound Poisson risks in case the mean, variance and range of the claim size distribution are known. They are based on stop-loss extremal distributions and improve the bounds derived earlier from dangerous extremal distributions. The special bounds obtained in case the relative variance of the claim size is unknown, but its maximal value is known, are related to other actuarial results.

Date: 1996
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