When a utility function is state-dependent, ex ante preferences for acts cannot elicit unique subjective probabilities without auxiliary devices. This paper introduces ex-post strength-of-preferences for state-contingent decision outcomes. Then we prove that a consistency condition between ex...

The mean-variance utility postulates that random variables with the same mean and variance should be equally desirable. This paper presents and discusses necessary and sufficient preference-based axioms for the existence of mean-variance utility in which any condition on variances but...

This paper studies necessary and sufficient preference-based conditions for differentiability of risk averse (prudent, or temperate) von Neumann-Morgenstern utility functions. The very idea to devise those conditions is based on the reverse claim of an old observation by Arrow that a risk-averse...

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...

Unlike the traditional normative decision theories under risk, we are concerned with a unary relation, interpreted as subjective acceptability judgment, on the set of all joint probability distributions over two-attributed decision outcomes, where the first attribute describes final wealth...