We study a Mean-Risk model derived from a behavioral theory of Disappointment with multiple reference points. One distinguishing feature of the risk measure is that it is based on mutual deviations of outcomes, not deviations from a specific target. We prove necessary and sufficient conditions for strict first and second order stochastic dominance, and show that the model is, in addition, a Convex Risk Measure. The model allows for richer, and behaviorally more plausible, risk preference patterns than competing models with equal degrees of freedom, including Expected Utility (EU), Mean-Variance (MV), Mean-Gini (MG), and models based on non-additive probability weighting, such a Dual Theory (DT). For example, in asset allocation, the decision-maker can abstain from diversifying in a risky asset unless it meets a threshold performance, and gradually invest beyond this threshold, which appears more acceptable than the extreme solutions provided by either EU and MV (always diversify) or DT and MG (always plunge). In asset trading, the model allows no-trade intervals, like DT and MG, in some, but not all, situations. An illustrative application to portfolio selection is presented. The model can provide an improved criterion for Mean-Risk analysis by injecting a new level of behavioral realism and flexibility, while maintaining key normative properties.
Author(s): Alessandra Cillo, Philippe Delquié
Keywords: Risk analysis; Uncertainty modeling; Utility theory; Stochastic dominance; Convex risk measures