This paper studies the "dual" theory of the smooth ambiguity model introduced by Klibanoff et al. (Econometrica 73:1849-1892, 2005). Unlike the original model, we characterize attitudes toward ambiguity captured by second-order probabilities. First, we give a set of axioms to derive a dual representation of the smooth ambiguity model. Second, we present a characterization of ambiguity aversion. Last, as an application of our dual model to a portfolio problem, we conduct comparative static predictions which give sufficient conditions to guarantee that an increase in smooth ambiguity aversion decreases the optimal portfolio.
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