hero working papers

Niveloids and Their Extensions:Risk Measures on Small Domains

Number: 458
Year: 2012
Author(s): S. Cerreia-Vioglio, F. Maccheroni, M. Marinacci,and A. Rustichini
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