Abstract
The present study is motivated by the following practical problem in collective risk theory. Besides the problem of determining the distribution of the total amount of claims and its concrete by-products (reinsurance premiums, refund formulae for example), what is the influence of negative risk sums (e.g., in group life insurance: include or not include annuitants in a group contract). This note gives some qualitative answers by giving criteria for deciding this question in the form of inequalities. The quantitative aspect could be made effective for insurance models having numerically computable distributions [e.g., Compound Poisson distribution [Bertram (1981, 1983). Hürlimann (1985)] negative binomial distribution and others [Bertram (1981)]].
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