Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Optimal consumption and portfolio choice with ambiguity and anticipation
Information Sciences: an International Journal
Geometric programming with fuzzy parameters in engineering optimization
International Journal of Approximate Reasoning
Asset portfolio optimization using fuzzy mathematical programming
Information Sciences: an International Journal
Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming
Journal of Computational and Applied Mathematics
Using genetic algorithm to support portfolio optimization for index fund management
Expert Systems with Applications: An International Journal
Kernel methods for short-term portfolio management
Expert Systems with Applications: An International Journal
Hi-index | 0.00 |
Conventional portfolio optimization models have an assumption that the future condition of stock market can be accurately predicted by historical data. However, no matter how accurate the past data is, this premise will not exist in the financial market due to the high volatility of market environment. This paper discusses the fuzzy portfolio optimization problem where the asset returns are represented by fuzzy data. A mean-absolute deviation risk function model and Zadeh's extension principle are utilized for the solution method of portfolio optimization problem with fuzzy returns. Since the parameters are fuzzy numbers, the gain of return is a fuzzy number as well. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the return of the portfolio optimization problem. Based on the duality theorem and by applying the variable transformation technique, the pair of twolevel mathematical programs is transformed into a pair of ordinary one-level linear programs so they can be manipulated. It is found that the calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on, the greater the potential return. An example illustrates the whole idea on fuzzy portfolio optimization problem.