On the Continuity of Efficient Solution Mappings in Portfolio Optimization

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.