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This article investigates under what conditions an increase in ambiguity reduces demand for an uncertain asset (or raises demand for coinsurance). We find that the comparative statics of ambiguity and of risks have structural similarities under the smooth ambiguity aversion model (Klibanoff, Marinacci, and Mukerji, ()). The determinant condition on ambiguity preferences is analogous to that on risk preferences. However, the comparative statics have fundamental differences under the α‐maxmin model (Ghirardato, Maccheroni, and Marinacci, ()). When relative risk aversion is less than 1, only an increase in ambiguity, which broadens support for an investor's belief in the probability of the return distribution in the manner of a strong increase in risk, can reduce demand for an uncertain asset.

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Knowing how small a violation of stochastic dominance rules would be accepted by most individuals is a prerequisite to applying almost stochastic dominance criteria. Unlike previous laboratory-experimental studies, this paper estimates an acceptable violation of stochastic dominance rules with 939,690 real world data observations on a choice of deductibles in automobile theft insurance. We find that, for all policyholders in the sample who optimally chose a low deductible, the upper bound estimate of the acceptable violation ratio is 0.0014, which is close to zero. On the other hand, considering that most decision makers, such as 99% (95%) of the policyholders in the sample, optimally chose the low deductible, the upper bound estimate of the acceptable violation ratio is 0.0405 (0.0732). Our results provide reference values for the acceptable violation ratio for applying almost stochastic dominance rules. This paper was accepted by Manel Baucells, decision analysis.