A smooth model of decision making under ambiguity

We propose and characterize a model of preferences over acts such that the decision maker prefers act f to act g if and only if E-mu phi (E(pi)u circle f) >= E-mu phi (E(pi)u circle g), where E is the expectation operator, u is a von Neumann-Morgenstern utility function, phi is an increasing transformation, and mu is a subjective probability over the set Pi of probability measures pi that the decision maker thinks are relevant given his subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes toward pure risk are characterized by the shape of u, as usual, while attitudes toward ambiguity are characterized by the shape of phi. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures Pi. One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's paradox). The maxmin expected utility model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as a limiting case of our model with infinite ambiguity aversion. Two illustrative portfolio choice examples are offered.