On the Continuity of Efficient Solution Mappings in Portfolio Optimization

Jia Liu and Hongyu Yang ()
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Jia Liu: Faculty of Science, Civil Aviation Flight University of China, Guanghan 618307, China
Hongyu Yang: Faculty of Science, Civil Aviation Flight University of China, Guanghan 618307, China

Mathematics, 2025, vol. 13, issue 23, 1-24

Abstract: This paper investigates the stability of a portfolio optimization model. After obtaining explicit analytical expressions for the sets of efficient and weakly efficient portfolios and analyzing their structural characteristics, we developed a corresponding framework for stability analysis. Through this framework, we observed that the stability of the solution set mappings, including outer-semicontinuity, inner-semicontinuity and Lipschitz continuity, is closely related to the ranking of the assets’ expected returns. This understanding enables a shift in stability assessment from traditional numerical simulation towards algebraic verification of asset parameters, potentially offering a more effective approach for stability analysis in this class of models.

Keywords: multicriteria optimization; portfolio selection; semicontinuity; Lipschitz continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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