Application of the problem of moments to derive bounds on integrals with integral constraints |
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Authors: | MJ Goovaerts R Kaas |
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Institution: | Katholieke Universiteit Leuven, Belgium;University of Amsterdam, The Netherlands;University of Amsterdam, The Netherlands |
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Abstract: | Recently a lot of results (for a review see Goovaerts et al. (1983)) have been obtained for bounds on stop-loss premiums in case of incomplete information on the claim distribution.As a consequence some extremal distributions (depending on the retention limit) have been characterized. The extremal distributions for the stop-loss ordering in case of fixed values of the retention limit are obtained by means of deep results from the theory of convex analysis. In the present contribution it is shown, by means of some results from the problem of moments, how bounds on integrals with integral constraints can be obtained. We assume only the knowledge of the moments μ0, μ1, …, μn. |
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Keywords: | Moment problem Integral constraints Bounds on distribution functions |
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