An analytic derivation of admissible efficient frontier with borrowing. (English) Zbl 1146.91025

Summary: The admissible efficient portfolio selection problem for risky assets has been discussed by W. Zhang and Z. Nie [Appl. Math. Comput. 159, No. 2, 357–371 (2004; Zbl 1098.91065)]. In this paper, the admissible efficient portfolio model is proposed under the assumption that there exists the borrowing (money or a risk free asset) case. The admissible efficient frontiers are developed by the spreads of expected return and risk from admissible errors. The analytic forms of the admissible efficient frontiers when short sales are not allowed on all risky assets are derived from two cases: the borrowing with an upper bound constraint, or without an upper bound constraint. The influence on the admissible efficient frontier is explained under the different interest rates of the borrowing. The differences between the results with the borrowing and the results without the borrowing is revealed by a real numerical example.


91B28 Finance etc. (MSC2000)
90C20 Quadratic programming


Zbl 1098.91065
Full Text: DOI


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