Niveloids and Their Extensions:Risk Measures on Small Domains

Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci and Aldo Rustichini

No 458, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

Abstract: Given a functional defi?ned on a nonempty subset of an Archimedean Riesz space with unit, necessary and sufficient conditions are obtained for the existence of a (convex or concave) niveloid that extends the functional to the entire space. In the language of mathematical fi?nance, this problem is equivalent to the one of verifying if the policy adopted by a regulator is consistent with monetary risk measurement, when only partial information is available. Keywords: extension theorems, Daniell-Stone theorem, risk measures, variational preferences

Date: 2012
New Economics Papers: this item is included in nep-rmg
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