Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory

Two notions of fractional stochastic dominance (SD) were recently proposed by Muller et al. (2017) and Huang et al. (2020) based on mean-reducing spreads and the coefficient of absolute risk aversion, respectively. We formulate a general class of fractional SD generated by a convex transform, which includes those built from absolute or relative risk aversion as special cases, and this serves as a convenient technical tool for construction of new notions of fractional SD. We obtain equivalent conditions for a preference modeled by rank-dependent utility or cumulative prospect theory to be consistent with each notion of fractional SD. Furthermore, we provide an empirical estimator for the parameters in fractional SD relationships, and we illustrate this with a financial data analysis. (c) 2022 Elsevier B.V. All rights reserved.