The α-maxmin model is a prominent example of preferences under

Knightian uncertainty as it allows to distinguish ambiguity and ambiguity

attitude. These preferences are dynamically inconsistent for nontrivial

versions of α. In this paper, we derive a recursive, dynamically consistent

version of the α-maxmin model. In the continuous-time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level.

We study the properties of the utility function and provide an Arrow-

Pratt approximation of the static and dynamic certainty equivalent. We

derive a consumption-based capital asset pricing formula and study the

implications for derivative valuation under indifference pricing.