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Stochastic dominance is a preference relation of uncertain prospect definedover a class of utility functions. While this utility class represents basicproperties of risk aversion, it includes some extreme utility functions rarelycharacterizing a rational decision maker's preference. In this paper weintroduce reference-based almost stochastic dominance (RSD) rules which wellbalance the general representation of risk aversion and the individualizationof the decision maker's risk preference. The key idea is that, in the generalutility class, we construct a neighborhood of the decision maker's individualutility function, and represent a preference relation over this neighborhood.The RSD rules reveal the maximum dominance level quantifying the decisionmaker's robust preference between alternative choices. We also propose RSDconstrained stochastic optimization model and develop an approximationalgorithm based on Bernstein polynomials. This model is illustrated on aportfolio optimization problem.

Reference-Based Almost Stochastic Dominance Rules with Application in Risk-Averse Optimization