On behalf of the Scientific Committee of the de Finetti Risk Seminars, we are glad to invite you to participate at the following Lecture

Monetary Utility Functions with the CxLS (convex level sets) property

Freddy Delbaen

ETH Zurich, Switzerland

ABSTRACT Monetary utility functions are -- except for the expected value -- not of von Neumann-Morgenstern type. In case the utility function has convex level sets in the set of probability measures on the real line, we can give some characterisation that comes close to the vN-M form. For coherent utility functions this was solved by Ziegel. The general concave case under the extra assumptions of weak compactness, was solved by Stephan Weber. In the general case the utility functions are only semi continuous. Using the fact that law determined utility functions are monotone with respect to convex ordering, we can overcome most of the technical problems. The characterisation is similar to Weber's theorem except that we need vN_M utility functions that take the value $-\infty$. Having convex level sets can be seen as a weakened form of the independence axiom in the vN-M theorem. This is joint work with Bellini, Bignozzi and Ziegel.

LOCATION: The seminar will be held on Wednesday, March 18, at 18.00, Aula di rappresentanza, Dept. of Mathematics, Milano University, Via C. Saldini 50, Milano. A refreshment will be offered at 17.30.

Scientific Committee:

Prof. Marco Frittelli (Univ. degli Studi di Milano) Prof. Fabio Maccheroni (Univ. Bocconi) Prof. Massimo Marinacci (Univ. Bocconi) Prof. Emanuela Rosazza Gianin (Univ. Milano-Bicocca) Dott. Simone Cerreia-Voglio (Univ. Bocconi) Dott. Marco Maggis (Univ. degli Studi di Milano)

**************************************************** Emanuela Rosazza Gianin Dipartimento di Statistica e Metodi Quantitativi Università di Milano Bicocca Edificio U7 – 4° Piano Via Bicocca degli Arcimboldi, 8 20126 Milano

Tel. 02 64483208 Fax. 02 64483105 e-mail: emanuela.rosazza1@unimib.it

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