Almost stochastic dominance: Magnitude constraints on risk aversion

Abstract

Almost stochastic dominance (ASD) extends conventional first and second degree stochastic dominance by placing restrictions on the variability in the first and second derivatives of utility. Such restrictions increase the number of random variables for which a unanimous ranking of one over the other occurs. This paper advances an alternative approach to ASD in which the magnitude of absolute or relative risk aversion is constrained with both an upper bound and a lower bound. Using the results of Meyer (1977b), the paper provides cumulative distribution function (CDF) characterizations of these forms of ASD. Simple closed-form necessary and sufficient conditions for these ASD relations are determined for the special cases where the absolute or relative risk aversion is only bounded on one end or when the pair of random variables being compared have single-crossing CDFs. In addition, the relationship of the new ASD definitions to those in the literature is explored.