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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.

Suggested Citation

  • Fabio Maccheroni & Massimo Marinacci & Doriana Ruffino, 2011. "Does Uncertainty Vanish in the Small? The Smooth Ambiguity Case," Working Papers 391, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  • Handle: RePEc:igi:igierp:391
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    1. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    2. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    3. Machina, Mark J, 2001. "Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-260, November.
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