DYNAMICALLY CONSISTENT PREFERENCES WITH QUADRATIC BELIEFS

This article characterizes a family of preference relations over uncer tain prospects that (a) are dynamically consistent in the Machina sens e and moreover, for which the updated preferences are also members of this family and (b) can simultaneously accommodate Ellsberg- and Allai s-type paradoxes. Replacing the ''mixture independence'' axiom by ''mi xture symmetry,'' proposed by Chew, Epstein, and Segal (1991) for deci sion making under objective risk, and requiring that for some partitio n of the state space the agent perceives ambiguity and so prefers a ra ndomization over outcomes across that partition (proper uncertainty av ersion), preferences can be represented by a (proper) quadratic functi onal. This representation may be further refined to allow a separation between the quantification of beliefs and risk preferences that is cl osed under dynamically consistent updating.