Loss Aversion Robust Optimization Model Under Distribution and Mean Return Ambiguity

From the aspect of behavioral finance, which is an emerging area integrating human behavior into finance, this work studies a robust portfolio problem for loss-averse investors under distribution and mean return ambiguity. A loss-aversion distributionally-robust optimization model is constructed if the return distribution of risky assets is unknown. Then, under the premise that the mean returns of risky assets belong to an ellipsoidal uncertainty set, a model under joint ambiguity in distribution and mean returns is constructed. This study solves both robust models and derives their analytical solutions, respectively. Moreover, the effect of ambiguity aversion and loss aversion on robust optimal portfolio returns is studied. The results show that ambiguity-neutral investors who do not know the return distribution obtain more robust optimal portfolio returns than ambiguity-averse investors who are unaware of both the distribution and mean return. The difference between them decreases with the increase of loss aversion coefficients and increases with ambiguity aversion coefficients. Both loss aversion and ambiguity aversion play important roles in investors' behavioral portfolio selection.