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Comparing risks with reference points: a stochastic dominance approach. (English) Zbl 1371.91059

Summary: This paper develops a stochastic dominance rule for the reference-dependent utility theory proposed by B. Kőszegi and M. Rabin [“Reference-dependent risk attitudes”, Am. Econ. Rev. 97, No. 4, 1047–1073 (2007; doi:10.1257/aer.97.4.1047)]. 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.

MSC:

91B16 Utility theory
91B30 Risk theory, insurance (MSC2010)
91G10 Portfolio theory
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