An Integrated Fuzzy Min-Max Goal Programming Approach to Risk-Aware Portfolio Optimization

Abstract

Background Stock market investment is sometimes perceived as being dependent on luck, particularly when investors are unfamiliar with systematic investment strategies. However, mathematical models can provide a structured approach to stock selection and portfolio optimization. Investors often need to consider several factors simultaneously, including short-term returns, long-term returns, dividend income, and investment risk. Therefore, an appropriate mathematical optimization model is required to support investment decisions under uncertain market conditions. Methods This study develops a fuzzy goal programming model for portfolio optimization. The proposed model considers multiple investment objectives simultaneously. It aims to maximize short-term returns, long-term returns, and annual dividend income while minimizing investment risk. Min–max goal programming is employed to handle the multiple objectives and uncertain nature of stock market data. The proposed model is demonstrated using a real-life case study based on recent stock market data obtained from the Bombay Stock Exchange (BSE). Results The fuzzy goal programming model that has been proposed offers a systematic method for choosing stocks and for optimizing the investment portfolio. Since it takes into account returns, annual dividends, and investment risk at the same time, it is able to help in identifying an appropriate portfolio when market conditions are uncertain. A case study based on recent data from the Bombay Stock Exchange shows that the proposed approach can be used in supporting real investment decisions. Conclusions The use of fuzzy goal programming in conjunction with the min-max method provides a straightforward and systematic approach to multi-objective portfolio optimization when dealing with market uncertainty, taking into account both short-term and long-term returns, dividends, and risk.