Generalized Almost Stochastic Dominance

Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. However, the commonly used integral condition for almost seconddegree stochastic dominance does not map into the corresponding classes of increasing concave utility functions with bounded derivatives, nor does it inherit some appealing properties of stochastic dominance. We de…ne generalized almost second-degree stochastic dominance and almost second-degree risk in terms of the appropriate utility classes and derive the equivalent integral conditions. We also extend these concepts to higher degrees so that the desirable properties of stochastic dominance are preserved. Finally, we de…ne convex generalized almost stochastic dominance to deal with risk-loving preferences. Generalized almost stochastic dominance should be useful in empirical research (e.g., in …nance) and theoretical analysis of applied situations.