Fuzzy multi period portfolio selection with different rates for borrowing and lending

Investment strategic planning is one of the most important areas of research in financial engineering. The primary concern of this research is to determine the amount of investment in different planning areas especially when the rate of borrowing is greater than that of lending. The proposed research method in this paper is a form of fuzzy linear programming which is capable of determining the amount of investment in different time cycles. In this paper return rates and borrowing/lending rate are presented as fuzzy triangular numbers instead of crisp representations. The developed model can instruct the balance between cash and margin for investors and using fuzzy set theory, their confidence level can be obtained for each produced portfolio. The method is also implemented using some numerical examples and the output results are discussed.