Modifying the Mean-Variance Approach to Avoid Violations of Stochastic Dominance

The mean-variance approach is an influential theory of decision under risk proposed by Markowitz (1952). Unfortunately, the mean-variance approach allows for violations of the first-order stochastic dominance. This paper proposes a new model in the spirit of the classical mean-variance approach but without violations of stochastic dominance. The proposed model represents preferences by a functional U(L)-ρ·r (L), where U(L) denotes the expected utility of a lottery L, ρ∈[-1,1] is a constant and r(L) is the mean absolute (utility) semideviation of lottery L. The model is interpreted as a linear trade-off between expected utility and utility dispersion. The model allows for the Allais paradox, violations of betweenness and switching behavior in the Samuelson's example.