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This paper establishes some equivalent relationships for the first three orders of the almost stochastic dominance (ASD). Using these results, we first prove formally that the ASD definition modified by Tzeng et al. (2012) does not possess any hierarchy property. Thereafter, we conclude that when the first three orders of ASD are used in the prospects comparison, investors prefer the one with positive gain, smaller variance and positive skewness. This information, in turn, enables decision makers to determine the ASD relationship among prospects when they know the moments of the prospects.
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