This paper first extends the theory of almost stochastic dominance (ASD) to the first four orders. We then establish some equivalent relationships for the first four orders of the ASD. Using these results, we prove formally that the ASD definition modified by Tzeng et al.\ (2012) does not...

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...

This study establishes necessary conditions for Almost Stochastic Dominance criteria of various orders. These conditions take the form of restrictions on algebraic combinations of moments of the probability distributions in question. The relevant set of conditions depends on the relevant order...