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In the article four extreme variants of BMSF(TR) in which extreme transition rules are valid, i.e. rules of maximum/minimum advancement and maximum/minimum fall, are presented. These four systems allow us to determine the lowest and highest expected premium in any insurance year in any BMSF(TR) and the intervals of values of expected premium in the systems of BMSF(TR) type which are modifications of these four extreme systems.
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