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Niveloids and Their Extensions:Risk Measures on Small Domains

Author

Listed:
  • Simone Cerreia-Vioglio
  • Fabio Maccheroni
  • Massimo Marinacci
  • Aldo Rustichini

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

Suggested Citation

  • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2012. "Niveloids and Their Extensions:Risk Measures on Small Domains," Working Papers 458, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:458
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    References listed on IDEAS

    as
    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Risk Measures: Rationality and Diversification," Carlo Alberto Notebooks 100, Collegio Carlo Alberto.
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    10. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Complete Monotone Quasiconcave Duality," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 321-339, May.
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    Keywords

    extension theorems; daniell-stone theorem; risk measures; variational preferences;
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