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

DOI10.1016/0377-0427(87)90145-2zbMath0633.65150OpenAlexW1988991636MaRDI QIDQ1096377

Rob Kaas, Marc J. Goovaerts

Publication date: 1987

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(87)90145-2

zbMATH Keywords

convex analysisstop-loss premiumsmoment constraintsactuarial sciencesclaim distributiondistributions with fixed moments

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Numerical methods for integral transforms (65R10) Moment problems (44A60) Probabilistic methods, stochastic differential equations (65C99) Statistical distribution theory (62E99)

Cites Work

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• Best bounds on the stop-loss premium in case of known range, expectation, variance and mode of the risk
• Upper bounds on stop-loss premiums in case of known moments up to the fourth order
• Extremal values of stop-loss premiums under moment constraints
• Application of the problem of moments to derive bounds on integrals with integral constraints
• A class of orthogonal polynomials
• Duality theory for bounds on integrals with applications to stop-loss premiums

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