On the Interplay between Distortion, Mean Value and Haezendonck-Goovaerts Risk Measures

21 Pages Posted: 25 Jul 2011 Last revised: 20 Mar 2012

See all articles by Marc Goovaerts

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Daniël Linders

University of Illinois

Koen Van Weert

Catholic University of Leuven (KUL). Faculty of Business and Economics

Fatih Tank

Ankara University - Department of Statistics

Date Written: July 25, 2011

Abstract

In actuarial research, distortion-, mean value- and Haezendonck-Goovaerts risk measures are concepts that are usually treated separately. In this paper we indicate and characterize the relation between the different risk measures, as well as their relation to convex risk measures. While it is known that the mean value principle can be used to generate premium calculation principles, we will show how they also allow to generate solvency calculation principles. Moreover, we explain the role provided for the distortion risk measures as an extension of the Tail Value-at-Risk (TVaR) and Conditional Tail Expectation (CTE).

Suggested Citation

Goovaerts, Marc and Linders, Daniël and Van Weert, Koen and Tank, Fatih, On the Interplay between Distortion, Mean Value and Haezendonck-Goovaerts Risk Measures (July 25, 2011). Insurance: Mathematics and Economics, Vol. 51, No. 1, pp. 10-18, Available at SSRN: https://ssrn.com/abstract=1894686 or http://dx.doi.org/10.2139/ssrn.1894686

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Daniël Linders (Contact Author)

University of Illinois ( email )

306 Altgeld Hall,
1409 West Green Street
Champaign, IL 61822
United States

Koen Van Weert

Catholic University of Leuven (KUL). Faculty of Business and Economics ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Fatih Tank

Ankara University - Department of Statistics ( email )

Ankara, Tandogan 06100
Turkey

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