演講訊息 TALKS

摘要： 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 characterization that comes close to the vN-M form. For coherent utility functions this was solved by Ziegel. The concave case under the extra assumptions of weak compactness, was solved by Stephan Weber. Using the fact that law determined utility functions are monotone with respect to convex ordering, we could give a complete characterization. The characterization is similar to Weber's theorem except that we need concave 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 theory. It is a property that is related to elicitability as used in statistics. (joint work with Bellini, Bignozzi and Ziegel, paper accepted in Finance and Stochastics)