Articles

Characterizations of Smooth Ambiguity Based on Continuous and Discrete Data

S. MINARDI, A. SAVOCHKIN

Mathematics of Operations Research

February 2017, vol. 42, n°1, pp.167-178

Departments: Economics & Decision Sciences

Keywords: smooth ambiguity; variational preferences; revealed preference; completely monotone functions; Afriat inequalities; moment problem

https://pubsonline.informs.org/doi/pdf/10.1287/moor.2016.0799


In the Anscombe-Aumann setup, we provide conditions for a collection of observations to be consistent with a well-known class of smooth ambiguity preferences (Klibanoff P, Marinacci M, Mukerji S (2005) A smooth model of decision making under ambiguity. Econometrica 73(6):1849–1892.). Each observation is assumed to take the form of an equivalence between an uncertain act and a certain outcome. We provide three results that describe these conditions for data sets of different cardinality. Our findings uncover surprising links between the smooth ambiguity model and classic mathematical results in complex and functional analysis.


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