Decision theory under ambiguity

We review recent advances in the field of decision making under

uncertainty or ambiguity. We start with a presentation of the general approach to a

decision problem under uncertainty, as well as the ‘standard’ Bayesian treatment

and issues with this treatment. We present more general approaches (Choquet

expected utility, maximin expected utility, smooth ambiguity and so forth) that

have been developed in the literature under the name of models of ambiguity

sensitive preferences. We draw a distinction between fully subjective models

and models incorporating explicitly some information. We review definitions

and characterizations of ambiguity aversion in these models. We mention the

challenges posed by some of the models presented. We end with a review of

part of the experimental literature and applications of these models to economic

settings.