Fuzzy portfolio optimization under downside risk measures

Authors:
Enriqueta Vercher;José D. Bermúdez;José Vicente Segura
Affiliations:
Departament d'Estadística i Investigació Operativa, Universitat de València, Avgda. Vicent Andrés Estellés, s/n, 46100 Burjassot, Spain;Departament d'Estadística i Investigació Operativa, Universitat de València, Avgda. Vicent Andrés Estellés, s/n, 46100 Burjassot, Spain;Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. Ferrocarril s/n, 03202 Elche, Spain
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

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.