The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents' choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.
Bibliographical noteFunding Information:
An earlier version of this paper was entitled “Risk aversion for multiple-prior expected utility”. I gratefully acknowledge helpful comments of Michele Cohen, Rose-Anne Dana, Simon Grant, Ehud Lehrer, Isaco Meilijson, Klaus Nehring, and, in particular, Tomasz Strzalecki. I benefited from excellent referee reports of this journal. The research was supported by the NSF under Grant SES-0099206.
- Mean-independent risk
- Multiple-prior expected utility
- Risk aversion
- Variational preferences