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Mean-Variance Portfolio Selection with Reference Dependent Preferences

We study S-shaped utility maximization for the standard portfolio selection problem with one risky and one risk-free asset. We derive a mean-variance criterium of choice, which preserves reference dependence and the reflection effect. Subsequently, we study diversification possibilities and obtain the demand for the risky asset. We close the paper with an alternative interpretation of the criterium in terms of target-based decision making.