A constraint-free approach to optimal reinsurance

Details

Serval ID
serval:BIB_AAE052904D3B
Type
Article: article from journal or magazin.
Collection
Publications
Title
A constraint-free approach to optimal reinsurance
Journal
Scandinavian Actuarial Journal
Author(s)
Gerber H.U., Shiu E.S.W., Yang H.
ISSN
0346-1238
1651-2030
Publication state
Published
Issued date
02/01/2019
Peer-reviewed
Oui
Volume
2019
Number
1
Pages
62-79
Language
english
Abstract
Reinsurance is available for a reinsurance premium that is determined according to a convex premium principle H. The first insurer selects the reinsurance coverage that maximizes its expected utility. No conditions are imposed on the reinsurer's payment. The optimality condition involves the gradient of H. For several combinations of H and the first insurer's utility function, closed-form formulas for the optimal reinsurance are given. If H is a zero utility principle (for example, an exponential principle or an expectile principle), it is shown, by means of Borch's Theorem, that the optimal reinsurer's payment is a function of the total claim amount and that this function satisfies the so-called 1-Lipschitz condition. Frequently, authors impose these two conclusions as hypotheses at the outset.
Keywords
Optimal reinsurance, expected utility, convex premium principle, Borch's theorem, Pareto-optimal risk exchange, constraint-free approach
Web of science
Create date
05/09/2018 10:56
Last modification date
21/08/2019 6:14
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