Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/227834
Authors: 
Nendel, Max
Schmeck, Maren Diane
Riedel, Frank
Year of Publication: 
2020
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 638
Abstract: 
In this paper, we provide an axiomatic approach to general premium priciples giving rise to a decomposition into risk, as a generalization of the expected value, and deviation, as a generalization of the variance. We show that, for every premium priciple, there exists a maximal risk measure capturing all risky components covered by the insurance prices. In a second step, we consider dual representations of convex risk measures consistent with the premium priciple. In particular, we show that the convex conjugate of the aforementioned maximal risk measure coincides with the convex conjugate of the premium principle on the set of all finitely additive probability measures. In a last step, we consider insurance prices in the presence of a not neccesarily frictionless market, where insurance claims are traded. In this setup, we discuss premium principles that are consistent with hedging using securization products that are traded in the market.
Subjects: 
Principles of premium calculation
risk measure
deviation measure
convexduality
superhedging
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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