Risk Aversion for Multiple-Prior Expected Utility

The objective of this paper is to identify 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 (2005). We show that a necessary and sufficient condition for risk aversion of concave multiple-prior expected utility under probability measure π is that the set of probability priors be π-stable. The property of π-stability is a new concept. We show that cores of convex distortions of a probability measure have that property. Relative entropy neighborhoods - used in the context of model uncertainty - have it, too, but Euclidean neighborhoods fail to have it. We also show that the existence of a non-trivial unambiguous event precludes risk aversion with respect to any prior.

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