Does Uncertainty Vanish in the Small? The Smooth Ambiguity Case

Fabio Maccheroni, Massimo Marinacci and Doriana Ruffino

No 391, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

Abstract: We study orders of risk and model uncertainty aversion in the smooth ambiguity model proposed by Klibano, Marinacci, and Mukerji [4]. We consider a quadratic approximation of their model and we show that both risk and model uncertainty attitudes have at most a second order effect. Specifically, the order depends on the properties of the support of the decision maker's limit prior, which we fully characterize. We find that model uncertainty attitudes have a second order effect unless the support is a singleton, that is, unless model uncertainty fades away in the limit. Special attention is given to the binomial state spaces often used in mathematical finance.

Date: 2011
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