Goovaerts, M. J.; Haezendonck, J.; de Vylder, F. Numerical best bounds on stop-loss premiums. (English) Zbl 0498.62089 Insur. Math. Econ. 1, 287-302 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 14 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 90C05 Linear programming 90C90 Applications of mathematical programming Keywords:numerical best bounds; stop-loss premiums; infinite number of linear inequality constraints; retention limit; unimodal distribution; concave functions; dual problem PDFBibTeX XMLCite \textit{M. J. Goovaerts} et al., Insur. Math. Econ. 1, 287--302 (1982; Zbl 0498.62089) Full Text: DOI References: [1] Buhlmann, H., Ein anderer Beweis für die Stop-Loss-Ungleichung in der Arbeit Gagliardi/Straub, Mitt. der Ver. Schw. Vers. Math., 74, 284-285 (1974) [2] Bowers, N. L., An upper bound on the stop-loss net premium, Trans. Soc. Actuaries, 21, 211-216 (1969) [3] De Groot, R., Ongelijkheden voor stop-loss premies gebaseerd op E.-T. systemen in het kader van de veralgemeende convexe analyse, (Thesis Nr. 34 (1979), Faculteit Econ. en Toeg. Econ: Faculteit Econ. en Toeg. Econ Wetenschappen K.U. Leuven) [4] De Vylder, F., Best upper bounds for integrals with respect to measures allowed to vary under conical and integral constraints, Insurance Math. Econom., 1, 2, 109-130 (1982) · Zbl 0488.49030 [5] De Vylder, F. (subm.). Duality theory for bounds on integrals with applications to stop-loss premiums. Scand. Actuarial J.; De Vylder, F. (subm.). Duality theory for bounds on integrals with applications to stop-loss premiums. Scand. Actuarial J. · Zbl 0522.62087 [6] De Vylder, F.; Goovaerts, M., Upper and lower bounds on stop-loss premiums in case of known expectation and variance of the risk variable, Mitt. der Ver. Schw. Vers. Math. Heft, 1, 149-165 (1982) · Zbl 0487.62087 [7] De Vylder, F.; Goovaerts, M., Analytical best upper bounds for stop-loss premiums, Insurance Math. Econom., 1, 3, 197-211 (1982), 1982 · Zbl 0508.62088 [8] Ekeland, I.; Temam, R., Convex Analysis and Variational Problems (1976), North-Holland: North-Holland Amsterdam [9] Gagliardi, B.; Straub, E., Ein obere Grenze für Stop-Loss-Prämien, Mitt. Ver. Schw. Vers. Math., 74, 215-221 (1974) · Zbl 0321.62104 [10] Goovaerts, M.; De Vylder, F., Upper bounds on stop-loss premiums under constraints on claim size distribution as derived from representation theorems for distribution functions, Scand. Actuarial J., 141-148 (1980) · Zbl 0446.62107 [11] Heilman, W. R., Improved methods for calculating and estimating maximal stop-loss premiums, Blätter Deutschen Ges. Vers. Math., 21-49 (1981) [12] Ioffe, A. D.; Tihomorov, V. M., Theory of Extremal Problems (1979), North-Holland: North-Holland Amsterdam [13] Taylor, G. C., Upper bounds on stop-loss premiums under constraints on claim size distribution, Scand. Actuarial J., 94-105 (1977) · Zbl 0369.62111 [14] Verbeek, H., A stop-loss inequality for compround Poisson processes with a unimodal claimsize distribution, ASTIN Bull., 9, 247-256 (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.