The resolution of excess investment in Fuzzy portfolio selection using piecewise linear function

Abstract

Fuzzy portfolio selection on the guaranteed return rate has been proposed to study excess investment in different dimensions of risk preferences. However, the theory of behavioural finance proposes that the investment proportions of securities are not only determined by the intrinsic value of the security but also largely affected by the behaviour of investors. Therefore, the investment behaviour of an investor in the fuzzy portfolio selection should be considered in the excess investment for different securities at different return rates. In this study, we propose a piecewise linear function for the fuzzy expected return rates and use the new decision variables for investment proportion in each security. In addition, considering the investment behaviours of decision-makers, we use the concept of fuzzy contingent strategy to take into account the relationships of investment proportion among the securities in the fuzzy portfolio selection. Analysis results indicated that we can find the investment proportions in the portfolio with the possible results of shortage investment, full investment, or excess investments by the fuzzy constraint of total investment proportions. Finally, in the illustration with two experiments, investors could individually select the portfolio by the piecewise linear function in shortage investment, full investment, or excess investment.

Keywords

• Fuzzy portfolio selection
• excess investment
• guaranteed return rate
• piecewise linear function
• contingent strategy
• 08A72