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Bounds on Modified Stop-Loss Premiums in Case of Known Mean and Variance of the Risk Variable

Published online by Cambridge University Press:  29 August 2014

F. De Vylder ,
M. Goovaerts  and
N. De Pril
F. De Vylder
Affiliation:
U.C. Louvain and K.U. Leuven, Belgium
M. Goovaerts
Affiliation:
U.C. Louvain and K.U. Leuven, Belgium
N. De Pril
Affiliation:
U.C. Louvain and K.U. Leuven, Belgium
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Abstract

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In case of a stop-loss treaty the reinsurer takes over that part of the risk that exceeds a given amount y1. We will deduce bounds on a modified stop-loss treaty where the liability of the reinsurer is limited to y2–y1 in case the claim amount exceeds y2. Upper and lower bounds of this modified stop-loss premium are obtained as a simple application of results obtained earlier by the first author.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 13 , Issue 1 , June 1982 , pp. 23 - 36
Copyright
Copyright © International Actuarial Association 1982

References

Bowers, N. L. Jr. (1969). An upper bound on the stop-loss net premium. Transactions of the Society of Actuaries, 21, 211–217.Google Scholar
De Vylder, F. (1982). Best upper bounds for integrals with respect to measures allowed to vary under conical and integral constraints. Insurance: Mathematics and Economics, 1 (2), 109–130.Google Scholar
De Vylder, F. and Goovaerts, M. (1982a). 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., 149–164.Google Scholar
De Vylder, F. and Goovaerts, M. (1982b). Analytical best upper bounds for stop-loss premiums. Insurance: Mathematics and Economics, 1 (3), 197–211.Google Scholar