Abstract
At the 1990 ASTIN-colloquium, Schmitter posed the problem of finding the extreme values of the ultimate ruin probability Iˆ(u) in a risk process with initial capital u, fixed safety margin I¸, and mean I¼ and variance Iƒ2 of the individual claims. This note aims to give some more insight into this problem. Schmitter's conjecture that the maximizing individual claims distribution is always diatomic is disproved by a counterexample. It is shown that if one uses the distribution maximizing the upper bound e−Ru to find a ‘large’ ruin probability among risks with range [0, b], incorrect results are found if b is large or u small. The related problem of finding extreme values of stop-loss premiums for a compound Poisson (I») distribution with identical restrictions on the individual claims is analyzed by the same methods. The results obtained are very similar.
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