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Recursive Preferences and Ambiguity Attitudes

We study the implications of recursivity and state monotonicity in intertemporal consumption problems under ambiguity. We show that monotone recursive preferences admit a recursive and ex-ante representation, both with translation invariant certainty equivalents. Translation invariance restricts the decision maker's absolute ambiguity attitudes to be constant. As a byproduct, this restriction implies that monotone recursive and convex preferences collapse to the variational model. Using dynamic consistency, we show that our two representations are connected by a condition that extends the standard rectangularity notion for recursive multiple priors. This "generalized rectangularity" condition allows us to uniquely retrieve the ex-ante representation starting fromthe recursive one and to obtain dynamic consistency conditions for preferences exhibiting constant absolute ambiguity aversion. Interpreting generalized rectangularity as a law of iterated nonlinear expectations, we discuss its relevance with respect to large sample theory.

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