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Document Details :

Title: The Schmitter Problem and a Related Problem
Subtitle: A Partial Solution
Author(s): KAAS, R.
Journal: ASTIN Bulletin
Volume: 21    Issue: 1   Date: April 1991   
Pages: 133-146
DOI: 10.2143/AST.21.1.2005406

Abstract :
At the 1990 ASTIN-colloquium, SCHMITTER posed the problem of finding the extreme values of the ultimate ruin probability ψ (u) in a risk process with initial capital u, fixed safety margin 0, and mean &mu and variance &sigma2 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 dlatomic 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 (λ) distribution with identical restrictions on the individual claims is analyzed by the same methods. The results obtained are very similar.