A note on natural risk statistics

Authors:
Shabbir Ahmed;Damir Filipović;Gregor Svindland
Affiliations:
H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States;Vienna Institute of Finance, University of Vienna, Austria and Vienna University of Economics and Business Administration, Heiligenstädter Strasse 46-48, 1190 Wien, Austria;Mathematics Institute, University of Munich, Theresienstrasse 39, 80333 München, Germany
Venue:
Operations Research Letters
Year:
2008

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Abstract

Recently Heyde, Kou and Peng [C.C. Heyde, S.G. Kou, X.H. Peng, What is a good external risk measure: Bridging the gaps between robustness, subadditivity, and insurance risk measures, 2007, preprint.] proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternate proofs of the representation results regarding natural risk statistics.