Comparing risks with reference points: A stochastic dominance approach

This paper develops a stochastic dominance rule for the reference-dependent utility theory proposed by Kőszegi and Rabin (2007). The new ordering captures the effects of loss aversion and can be used as a semi-parametric approach in the comparison of risks with reference points. It is analytically amenable and possesses a variety of intuitively appealing properties, including the abilities to identify both "increase in risk" and "increase in downside risk", to resolve the Allais-type anomalies, to capture the violation of translational invariance and scaling invariance, and to accommodate the endowment effect for risk. The generalization to third-order dominance reveals that loss aversion can either reinforce or weaken prudence, depending on the location of the reference point. Potential applications of the new ordering in financial contexts are briefly discussed.