Abstract
Higher-order differentiability is one of the common properties of von Neumann Morgenstern (vNM) utility functions used in economic applications. In particular, it is indispensable to analyze higher-order attitudes toward risk. We shall study three classes of finite-order differentiable vNM utility functions. Then we shall discuss simple and behaviorally interpretable conditions which are necessary and sufficient for a vNM utility function to belong to one of those three classes.
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