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This paper denes local aversion to a risk index. I show that the local aversion to the Aumann and Serrano [2008] index of riskiness coincides with absolute risk aversion, and that the same applies for the Foster and Hart [2009] measure of riskiness. Using this \local consistency I oer a new approach for axiomatizing the Aumann and Serrano index of riskiness and present other applications of this approach for relative risk aversion, \tardiness (time preferences) and the appeal of information.
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