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Fuzzy portfolio optimization under downside risk measures. (English) Zbl 1190.91140

Summary: This paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return. We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means. We establish the relationship between those mean-interval definitions for a given fuzzy portfolio by using suitable ordering relations. Finally, we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form.

MSC:

91G10 Portfolio theory
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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