A new method for deriving bounds for integrals with respect to measures allowed to vary under conical and integral constraints

摘要

In insurance literature on applied mathematics in actuarial sciences the theory of convex analysis is applied to so called stop-loss premiums in case only some moments of the claim distribution are known, possibly combined with other conical characteristics of the distribution. In the present contribution a much simpler method is proposed, based on results from the theory of the problem of moments. The resulting algorithm can handle an arbitrary number of moment constraints, thus considerably generalizing results obtained previously.