Bhuvnesh Khatana
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India.

Geetanjali Panda
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India.

DOI https://doi.org/10.33889/IJMEMS.2026.11.1.001

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Abstract

This paper presents a methodology for determining the optimal portfolio that maximizes the Sharpe ratio within a bilevel framework. The upper-level of the model maximizes the Sharpe ratio of the portfolio, while the lower-level minimizes the risk for a given expected return, which is treated as a parameter. In the methodology, a gradient-based active set approach is proposed to solve the bilevel portfolio optimization model. The proposed method generates a sequence of portfolios converging to the optimal portfolio. To validate the method, the results are tested and verified using real-world portfolio datasets collected from the Bombay Stock Exchange, India. It is observed in the numerical experiment that the Sharpe ratio obtained in a bilevel framework is better than that of the traditional method.

Keywords- Bilevel optimization problem, Portfolio selection problem, Sharpe ratio, Markowitz model.

Citation

Khatana, B., & Panda, G. (2026). Active Set Approach for a Bilevel Portfolio Optimization Model. International Journal of Mathematical, Engineering and Management Sciences, 11(1), 1-14. https://doi.org/10.33889/IJMEMS.2026.11.1.001.