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Best upper bounds for integrals with respect to measures allowed to vary under conical and integral constraints. (English) Zbl 0488.49030


MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
49J27 Existence theories for problems in abstract spaces
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
26B25 Convexity of real functions of several variables, generalizations
90C55 Methods of successive quadratic programming type
90C25 Convex programming
49J45 Methods involving semicontinuity and convergence; relaxation
28B99 Set functions, measures and integrals with values in abstract spaces
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References:

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[2] Heilmann, W. R., Improved methods for calculating and estimating maximal stop-loss premiums, Blatter der Deutschen Gesellschaft für Versicherungsmathematik, 29-41 (1981) · Zbl 0485.62114
[3] Mulholland, H. P.; Rogers, C. A., Representation theorems for distribution functions, Proceedings London Mathematical Society, 178-223 (1958) · Zbl 0084.32902
[4] Taylor, G. C., Upper bounds on stop-loss premiums under constraints on claim size distribution, Scandinavian Actuarial Journal, 94-105 (1977) · Zbl 0369.62111
[5] De Vylder, F.; Goovaerts, M. J., Analytical best upper bounds on stop-loss premiums, Insurance: Mathematics and Economics, 1, 3 (1982), to appear · Zbl 0508.62088
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