A Circumscribed Ellipsoid Method for Multiobjective Programming and Applications to Financial Planning
Theodore B. Trafali̇s, Tsutomu Mishina · Contributions to management science · 1997
This paper proposes a portfolio selection model for common stock investments. Although the usage of the beta coefficient in the capital asset pricing model (CAPM) has its limitations, still it is one of the most powerful tools in financial planning. In the proposed model, individual beta has a range described as a tolerance and the different combinations of betas form scenarios. The objective of the model is to find the portfolio with the lowest unsystematic risk and the least conflicting solution among scenarios at the investor’s best knowledge. The problem is solved through an interactive multiobjective programming approach based on a circum scribed ellipsoid interior point algorithm. In the process of solving the problem, the investor can appropriately incorporate any information regarding the securities and the investor’s preference.