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Does Uncertainty Vanish in the Small? The Smooth Ambiguity Case

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  • Fabio Maccheroni
  • Massimo Marinacci
  • Doriana Ruffino

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.

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Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 391.

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Date of creation: 2011
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Handle: RePEc:igi:igierp:391

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  1. Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November.
  2. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
  3. Uzi Segal & Avia Spivak, 1988. "First Order Versus Second Order Risk Aversion," UCLA Economics Working Papers 540, UCLA Department of Economics.
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