Niveloids and their extensions: Risk measures on small domains

S. Cerreia-Vioglio; F. Maccheroni; M. Marinacci; A. Rustichini

doi:10.1016/j.jmaa.2013.11.034

Niveloids and their extensions: Risk measures on small domains

S. Cerreia-Vioglio, F. Maccheroni, M. Marinacci, A. Rustichini

Economics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

Given a functional defined 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 finance, 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.

Original language	English (US)
Pages (from-to)	343-360
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	413
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2013.11.034
State	Published - May 1 2014

Bibliographical note

Funding Information:
We thank an associate editor and two anonymous referees for very useful feedback, Giulia Brancaccio and Veronica Cappelli for helpful suggestions, Hans Föllmer and Alex Schied for encouragement, the participants of the Bachelier Course Robust Decision Theory and Risk Measurement (IHP Paris, 2012) for stimulating discussions. The financial support of ERC (Advanced Grant BRSCDP-TEA) and of the AXA-Bocconi Chair in Risk is gratefully acknowledged.

Keywords

Daniell-Stone Theorem
Extension theorems
Risk measures
Variational preferences

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10.1016/j.jmaa.2013.11.034

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abstract = "Given a functional defined 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 finance, 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.",

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AU - Cerreia-Vioglio, S.

AU - Maccheroni, F.

AU - Marinacci, M.

AU - Rustichini, A.

N1 - Funding Information: We thank an associate editor and two anonymous referees for very useful feedback, Giulia Brancaccio and Veronica Cappelli for helpful suggestions, Hans Föllmer and Alex Schied for encouragement, the participants of the Bachelier Course Robust Decision Theory and Risk Measurement (IHP Paris, 2012) for stimulating discussions. The financial support of ERC (Advanced Grant BRSCDP-TEA) and of the AXA-Bocconi Chair in Risk is gratefully acknowledged.

PY - 2014/5/1

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N2 - Given a functional defined 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 finance, 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.

AB - Given a functional defined 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 finance, 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.

KW - Daniell-Stone Theorem

KW - Extension theorems

KW - Risk measures

KW - Variational preferences

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JF - Journal of Mathematical Analysis and Applications

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ER -

Niveloids and their extensions: Risk measures on small domains

Abstract

Bibliographical note

Keywords

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