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Improved methods for calculating and estimating maximal stop-loss premiums. (English) Zbl 0485.62114


MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics

Keywords:

optimization
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References:

[1] Bowers Jr.,N. L.: An Upper Bound on the Stop-Loss Net Premium. TSA 21, 211–216 (1969).
[2] Bühlmann, H.: Ein anderer Beweis für die Stop-Loss-Ungleichung in der Arbeit Gagliardi/ StrÄub. MVSV 74, 284–285 (1974).
[3] Bühlmann, H., D. Gagliardi, H. U. Gerber, andE. Straub: Some Inequalities for Stop-loss Premiums. The ASTIN Bulletin 9, 75–83 (1977).
[4] De Vylder, F.: Semi-continuous Linear Programming. MVSV 78, 39–53 (1978). · Zbl 0377.90069
[5] De Vylder, F.: Illustrations of the Duality Technique in Semi-continuous Linear Programming. Lecture presented at the ASTIN Colloquium, Taormina, 1978.
[6] Gagliardi, B. andE. Straub: Eine obere Grenze für Stop-Loss-PrÄmien. MVSV 74, 215–221 (1974). · Zbl 0321.62104
[7] Gerber, H. U.: On the Computation of Stop-Loss Premiums. MVSV 77, 47–58 (1977). · Zbl 0381.62090
[8] Goovaerts, M. J. andM. Declercq: On the Application of a Smoothing Inequality to the Estimation of Stop-loss Premiums. SAJ 33–40 (1980). · Zbl 0435.62105
[9] Heilmann, W.-R.: A Duality Theory for Stop-loss Distributions. SAJ 1978, 225–228. · Zbl 0396.62078
[10] Karlin, S. andW. J. Studden: Tchebycheff Systems: With Applications in Analysis and Statistics. Interscience Publishers, 1966. · Zbl 0153.38902
[11] Krabs, W.: Optimierung und Approximation. Teubner, 1975.
[12] Krein, M. G. and A. A. Nudelmann: The Markov Moment Problem and Extremal Problems. American Mathematical Society, 1977.
[13] Mauldin, R. D.: A representation Theorem for the Second Dual of C[0,1]. Studia Mathematica 46, 197–200 (1973). · Zbl 0255.46016
[14] Richter, H.: Parameterfreie AbschÄtzung und Realisierung von Erwartungswerten. BDGV 3, 147–162 (1957). · Zbl 0080.12603
[15] Seal, H. L.: Addendum to Bowers. TSA 21, 216–217 (1969).
[16] Taylor, G. C.: Upper Bounds on Stop-Loss Premiums under Constraints on Claim Size Distribution. SAJ 1977, 94–105. · Zbl 0369.62111
[17] Verbeek, H. G.: A Stop Loss Inequality for Compound Poisson Processes with a Unimodal Claimsize Distribution. The ASTIN Bulletin 9, 247–256 (1977).
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