Decomposition of General Premium Principles into Risk and Deviation

Nendel M, Schmeck MD, Riedel F (2020) Center for Mathematical Economics Working Papers; 638, aktual. Version July 2020.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper, we provide an axiomatic approach to general premium principles 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 principle, 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 principle. 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.

AMS 2010 Subject Classification: 91B30; 91G20; 46A20
Stichworte
Principle of premium calculation; risk measure; deviation measure; convex duality; superhedging
Erscheinungsjahr
2020
Band
638
Seite(n)
18
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2945081

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Nendel M, Schmeck MD, Riedel F. Decomposition of General Premium Principles into Risk and Deviation. Center for Mathematical Economics Working Papers. Vol 638 aktual. Version July 2020. Bielefeld: Center for Mathematical Economics; 2020.
Nendel, M., Schmeck, M. D., & Riedel, F. (2020). Decomposition of General Premium Principles into Risk and Deviation (Center for Mathematical Economics Working Papers, 638) aktual. Version July 2020. Bielefeld: Center for Mathematical Economics.
Nendel, M., Schmeck, M. D., and Riedel, F. (2020). Decomposition of General Premium Principles into Risk and Deviation. Center for Mathematical Economics Working Papers, 638, aktual. Version July 2020. Bielefeld: Center for Mathematical Economics.
Nendel, M., Schmeck, M.D., & Riedel, F., 2020. Decomposition of General Premium Principles into Risk and Deviation, Center for Mathematical Economics Working Papers, no.638, aktual. Version July 2020., Bielefeld: Center for Mathematical Economics.
M. Nendel, M.D. Schmeck, and F. Riedel, Decomposition of General Premium Principles into Risk and Deviation, Center for Mathematical Economics Working Papers, vol. 638, aktual. Version July 2020., Bielefeld: Center for Mathematical Economics, 2020.
Nendel, M., Schmeck, M.D., Riedel, F.: Decomposition of General Premium Principles into Risk and Deviation. Center for Mathematical Economics Working Papers, 638, aktual. Version July 2020. Center for Mathematical Economics, Bielefeld (2020).
Nendel, Max, Schmeck, Maren Diane, and Riedel, Frank. Decomposition of General Premium Principles into Risk and Deviation. aktual. Version July 2020. Bielefeld: Center for Mathematical Economics, 2020. Center for Mathematical Economics Working Papers. 638.
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2020-07-31T08:52:24Z
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