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Dynamically consistent preferences with quadratic beliefs. (English) Zbl 0889.90013
Summary: This article characterizes a family of preference relations over uncertain prospects that (a) are dynamically consistent in the Machina sense and, moreover, for which the updated preferences are also members of this family and (b) can simultaneously accommodate Ellsberg- and Allais-type paradoxes. Replacing the “mixture independence” axiom by “mixture symmetry”, proposed by S. H. Chew, L. G. Epstein, and U. Segal [Econometrica 59, No. 1, 139-163 (1991; Zbl 0744.90018)] for decision making under objective risk, and requiring that for some partition of the state space the agent perceives ambiguity and so prefers a randomization over outcomes across that partition (proper uncertainty aversion), preferences can be represented by a (proper) quadratic functional. This representation may be further refined to allow a separation between the quantification of beliefs and risk preferences that is closed under dynamically consistent updating.
MSC:
91B08 Individual preferences
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