Does Uncertainty Vanish in the Small? The Smooth Ambiguity Case
We study orders of risk and model uncertainty aversion in the smooth ambiguity model proposed by Klibano, Marinacci, and Mukerji . 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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- Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005.
"A Smooth Model of Decision Making under Ambiguity,"
Econometric Society, vol. 73(6), pages 1849-1892, November.
- Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
- 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.
- Segal, Uzi & Spivak, Avia, 1990.
"First order versus second order risk aversion,"
Journal of Economic Theory,
Elsevier, vol. 51(1), pages 111-125, June.
- Machina, Mark J, 2001. " Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-60, November.
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