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Minimal representation of insurance prices

Pichler, Alois and Shapiro, Alexander 2015. Minimal representation of insurance prices. Insurance: Mathematics and Economics 62 , pp. 184-193. 10.1016/j.insmatheco.2015.03.011

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This paper prices insurance contracts by employing law invariant, coherent risk measures from mathematical finance. We demonstrate that the corresponding premium principle enjoys a minimal representation. Uniqueness–in a sense specified in the paper–of this premium principle is derived from this initial result. The representations are derived from a result by Kusuoka, which is usually given for nonatomic probability spaces. We extend this setting to premium principles for spaces with atoms, as this is of particular importance for insurance. Further, stochastic order relations are employed to identify the minimal representation. It is shown that the premium principles in the minimal representation are extremal with respect to the order relations. The tools are finally employed to explicitly provide the minimal representation for premium principles, which are important in actuarial practice.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0167-6687
Date of Acceptance: 11 March 2015
Last Modified: 13 Mar 2019 12:50

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